Image stabilization apparatus and image pickup apparatus

ABSTRACT

An image stabilization apparatus has an angular velocity detector detecting an angular velocity applied thereto and outputting the angular velocity, an acceleration detector detecting an acceleration applied to the image stabilization apparatus and outputting the acceleration, a principal point calculation unit calculating a principal point position of a shooting optical system, an rotation angular velocity calculation unit calculating a rotation angular velocity component about the principal point of the shooting optical system based on an output of the angular velocity detector, a revolution angular velocity calculation unit calculating a revolution angular velocity component about an object based on the output of the acceleration detector and a calculation result of the rotation angular velocity calculation unit and correcting the calculated revolution angular velocity component according to the principal point position, and a controlling unit performing image stabilization control based on a difference between the rotation and corrected revolution angular velocity components.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an image stabilization apparatus whichprevents deterioration of a shot image by correcting an image blur dueto shake, and an image pickup apparatus including the imagestabilization apparatus.

2. Description of the Related Art

FIG. 18 is a view showing an outline of an image stabilization apparatusincluded in the conventional camera. A shake which occurs to the camerahas six degrees of freedom in total, which are rotational movements ofthree degrees of freedom constituted of pitching, yawing and rollingmovement, and translation movements of three degrees of freedomconstituted of movements in an X-axis, a Y-axis and a Z-axis directions.The image stabilization apparatuses which are commercialized at presentusually corrects the image blur due to the rotational movements of twodegrees of freedom constituted of pitching and yawing movements whichsignificantly influence image stabilization.

Movement of camera is monitored by an angular velocity sensor 130. Asthe angular velocity sensor, a piezoelectric vibration angular velocitysensor that detects a Coriolis force which is caused by rotation isgenerally used. The angular velocity sensor 130 contains three detectorswhich perform detection of pitching movement that is the rotation aroundthe Z-axis in FIG. 18, detection of yawing movement that is the rotationaround the Y-axis in FIG. 18, and detection of rolling movement that isthe rotation around the X-axis (optical axis) in FIG. 18.

When images blur due to shake is to be corrected, output of the angularvelocity sensor 130 is sent to a lens CPU 106, and a target driveposition of a correcting lens 101 for image stabilization is calculated.In order to drive the correcting lens 101 to the target drive position,instruction signals are sent to voltage drivers 161 x and 161 y, and thevoltage drivers 161 x and 161 y follow the instruction signal to drivelens drivers 120 x and 120 y. The position of the correcting lens 101 ismonitored by lens position detectors 110 x and 110 y, and is fed back tothe lens CPU 106. The lens CPU 106 performs positional control of thecorrecting lens 101 based on the target drive position and the positionof the correcting lens 101. By driving the correcting lens according tothe shake like this, the image blur caused by shake can be corrected.

However, in the aforementioned image stabilization apparatus, detectionof movement of camera due to shake is performed by only the angularvelocity sensor 130, and therefore, the angular movement (rotationalmovement) can be monitored, but movement which causes the optical axisto move parallel vertically or laterally (hereinafter, referred to asparallel movement) cannot be monitored. Accordingly, image stabilizationcan be performed only for the movements of the two degrees of freedomconstituted of pitching and yawing movements.

Here, about the image blur caused by parallel movement, the case ofperforming shooting by using a micro lens with a focal length of 100 mmwill be described as an example. When a landscape at infinity distanceis shot by using this lens, if the angular velocity sensor outputsubstantially 0.8 deg/s, the image plane moving velocity is about 1.40mm/s (=100×sin 0.8) from the focal length. Therefore, the width of themovement of the image plane due to angular movement when shooting withan exposure time of 1/15 second becomes 93 μm (=1.40 mm/15). Further, ifthe entire camera is moved parallelly in the vertical direction at 1.0mm/s in addition to the angular movement, shooting is not influenced bythe parallel movement velocity component, and an image blur due toparallel movement does not occur, since in the case of infinityshooting, the shooting magnification β is substantially zero.

However, when close-up shooting is performed for shooting a flower orthe like, the shooting magnification is very large, and the influence ofparallel movement cannot be ignored. For example, when the shootingmagnification is equal-magnification (β=1), and the moving velocity inthe vertical direction is 1 mm/s, the image on the image plane movesalso a moving velocity of 1 mm/s. The movement width in the image planeat the time of performing shooting with an exposure time of 1/15 secondbecomes 67 μm, and the image blur due to parallel movement cannot beignored.

Next, a general method (model and mathematical expression) whichexpresses the movement of an object in a space in a field of physics orengineering will be described. Here, about the model expressing movementof the object on a plane, an ordinary object will be described forfacilitating the description. In this case, if the three degrees offreedom of the object are defined, the movement and the position of theobject can be uniquely defined.

The first one is the model expressing a translation movement and arotational movement (see FIGS. 19A and 19B). In a fixed coordinatesystem O-XY in a plane with the axis of abscissa set as an X-axis andthe orthogonal axis set as a Y-axis, the position of the object can bedetermined if defining the three degrees of freedom: a position X(t) inthe X-axis direction; a position Y(t) in the Y-axis direction; and therotational angle θ(t) of the object itself are specified as shown inFIG. 19A. As shown in FIG. 19B, the movement of the object (velocityvector) can be expressed by three components of an X-axis directiontranslation velocity Vx(t) and a Y-axis direction translation velocityVy(t) of a reference point (principal point O₂) set on the object, and arotation angular velocity {dot over (θ)}(t) around the reference pointon the object. This model is the commonest.

The second one is the model expressing an instantaneous center ofrotation and a rotation radius (see FIG. 20). In the fixed coordinatesystem O-XY in an XY plane, the object is assumed to be rotating at arotation velocity {dot over (θ)}(t) with a rotation radius R(t) around acertain point f(t)=(X(t), Y(t)) being set as an instantaneous center ofrotation, at a certain instant. Like this, the movement within the planecan be expressed by a locus f(t) of the instantaneous center of rotationand the rotation velocity {dot over (θ)}(t) at the instant. This modelis often used in the analysis of a link mechanism in mechanics.

In recent years, cameras equipped with a function of correcting parallelmovement are proposed in Japanese Patent Application Laid-Open No.H07-225405 and Japanese Patent Application Laid-Open No. 2004-295027. Itcan be said that in Japanese Patent Application Laid-Open No.H07-225405, the movement of camera in a three-dimensional space isexpressed by a translation movement and a rotation movement based on themeasurement values of three accelerometers and three angular velocitysensors.

Further, in Japanese Patent Application Laid-Open No. 2004-295027, inthe movement of camera including angular movement and parallel movement,as illustrated in FIG. 2 of Japanese Patent Application Laid-Open No.2004-295027, a distance n of the rotational center from the focal planeis calculated. In mathematical expression (1) of Japanese PatentApplication Laid-Open No. 2004-295027, the angular movement amount whichoccurs when the focal plane is set as the rotation center is calculatedin the first half part, and the parallel movement amount which occursdue to translation movement is calculated in the latter half part. Theparallel movement amount of the latter half part is a correction termwhich is considered by being replaced with rotation in the positionalienated from the focal plane by a distance n. The method for obtainingthe position n of the rotation center in FIGS. 3A and 3B in JapanesePatent Application Laid-Open No. 2004-295027 uses the concept of aninstantaneous center which is frequently used in the mechanics, as themodel expressing the movement in the space. This is the idea that themovement in the space can be expressed by a succession of the rotationalmovement, that is, the movement in the space is a rotational movement ofa certain radius with a certain point as the center at the instant, andis the rotational movement with a certain radius with the next certainpoint as the center at the next instant. Therefore, it can be said thatin Japanese Patent Application Laid-Open No. 2004-295027, the movementof camera due to shake is modeled as a succession of the rotationalmovement having the instantaneous center.

However, the method described in Japanese Patent Application Laid-OpenNo. H07-225405 has the problem that the calculation amount for obtainingthe blur amount in the image plane becomes tremendous, and the algorithmof calculation becomes very complicated. Further, the correctioncalculation with respect to the optical axis direction blur (out offocus) is not mentioned. Further, it can be said that in Japanese PatentApplication Laid-Open No. 2004-295027, movement of camera is modeled asa succession of the rotational movement having the instantaneous centerof rotation as described above, and the problem of the model and themathematical expression is that as described in paragraph [0047] ofJapanese Patent Application Laid-Open No. 2004-295027 by itself, in thecase of F1F2 (the forces applied to two accelerometers), the rotationcenter position n becomes ∞, and calculation cannot be performed.Further, the fact that the rotation center position n is ∞ means thatthe movement due to the angle in the pitching direction or in the yawingdirection is absent, and this movement cannot be detected by the angularvelocity sensor. The correction amount can be calculated by using theoutput of the two acceleration sensors, but the precision is low and thecalculation amount becomes tremendous. Further, by the mathematicalexpression in this case, the correction calculation of the movement inthe optical axis direction cannot be made.

Further, with a change in principal point position of the shootingoptical system, the correction error component which will be describedlater is output from the acceleration sensor (accelerometer), butJapanese Patent Application Laid-Open No. H07-225405 and Japanese PatentApplication Laid-Open No. 2004-295027 do not have any correspondingtechnical disclosure.

SUMMARY OF THE INVENTION

The present invention is made in view of the aforementioned problems,and has an object to provide an image stabilization apparatus and animage pickup apparatus which enable accurate image stabilization withouta control failure, reduces a calculation amount, and enable imagestabilization calculation corresponding to a change of a principal pointposition of a shooting optical system, in whatever state an angular blurand a parallel blur may coexist.

In order to attain the aforementioned object, an image stabilizationapparatus according to an embodiment of the present invention adopts aconstitution having a shooting optical system that shoots an object, inwhich a principal point of the shooting optical system moves in anoptical axis direction of the shooting optical system, an angularvelocity detector that detects an angular velocity which is applied tothe image stabilization apparatus and outputs the angular velocity, anacceleration detector that detects an acceleration which is applied tothe image stabilization apparatus and outputs the acceleration, acalculation unit that calculates a position of a principal point of theshooting optical system, a first angular velocity calculation unit thatcalculates a first angular velocity component about the position of theprincipal point based on an output of the angular velocity detector, asecond angular velocity calculation unit that calculates a secondangular velocity component based on the output of the accelerationdetector, an calculation result of the first acceleration calculationunit and the position of the principal point, and a controlling unitthat performs image stabilization control based on a difference betweenthe first angular velocity component and the second angular velocitycomponent.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating a main part of an image pickupapparatus that is embodiment 1 according to the present invention.

FIG. 2 is a simplified diagram of a camera state projected to an XYplane of embodiment 1.

FIG. 3 is comprised of FIGS. 3A and 3B showing flowcharts illustratingan operation of embodiment 1.

FIG. 4A is a diagram illustrating a coordinate system fixed onto acamera.

FIG. 4B is a top view of the camera.

FIG. 4C is a front view of the camera.

FIG. 4D is a side view of the camera.

FIG. 5 is a view expressing only an optical system of the camera in athree-dimensional space.

FIGS. 6A and 6B are views illustrating a polar coordinate system and anorthogonal coordinate system of a principal point A.

FIG. 7 is a coordinate map at the time of being projected to an X₉Y₉plane and a Z₉X₉ plane.

FIG. 8 is a diagram illustrating a camera state projected to the X₉Y₉plane.

FIG. 9 is a diagram illustrating a camera state projected to the Z₉X₉plane.

FIG. 10 is a view of a camera initial state at an initial time t=0.

FIG. 11 is a view of a camera initial state in an O-XYZ coordinatesystem.

FIG. 12 is a basic explanatory diagram of a polar coordinate system.

FIG. 13 is a diagram illustrating a camera state which is projected to atwo-dimensional XY coordinate system.

FIG. 14 is a diagram illustrating a camera state projected to atwo-dimensional ZX coordinate system.

FIG. 15 is a diagram illustrating a change of a principal point positionof a shooting optical system corresponding to a change of an imagemagnification.

FIG. 16 is a diagram illustrating an effect of accelerometer outputcorrection by presence or absence of accelerometer output correction.

FIG. 17 is comprised of FIGS. 17A and 17B showing flowchartsillustrating an operation of embodiment 2 according to the presentinvention.

FIG. 18 is a view illustrating an image stabilization apparatus of acamera of a conventional example.

FIGS. 19A and 19B are diagrams illustrating definitions of an objectposition and an object velocity in an ordinary two-dimensionalcoordinate system.

FIG. 20 is a diagram illustrating a definition of an ordinary locus ofan instantaneous center of rotation.

DESCRIPTION OF THE EMBODIMENTS

Preferred embodiments of the present invention will now be described indetail in accordance with the accompanying drawings.

Aspects for carrying out the present invention are as shown in thefollowing embodiments 1 and 2.

Embodiment 1

In the following embodiment, the shake movement of the camera held byhuman hands, and an image movement which occurs on an image plane as aresult of the shake movement of the camera will be expressed by“rotation revolution movement expression” with the movement modelexpressing a rotation movement and a revolution movement and ageometrical-optical expression being combined.

The present embodiment is an image stabilization apparatus whichcalculates a camera movement from the measured values of anaccelerometer and an angular velocity sensor, and the rotationrevolution movement expression, and further calculates an imagemovement. By performing drive control of a part of the shooting lens ora part or whole of the image pickup device based on a calculated valueof the image movement, the image blur is corrected. Alternatively, thepresent invention provides an image stabilization apparatus whichcorrects an image blur by performing image processing of a shot imagebased on the calculated value of the image movement obtained from therotation revolution movement expression.

FIG. 1 is a block diagram illustrating a main part of an image pickupapparatus (camera system) including an image stabilization apparatusaccording to embodiment 1 of the present invention. The parts whichperform the same functions as in the conventional examples are assignedwith the same reference numerals and characters, and the redundantdescription will be properly omitted.

The image stabilization apparatus according to embodiment 1 is providedin a lens barrel 102 attachable to and detachable from a camera body201, and performs blur correction with respect to the directions of fivedegrees of freedom of pitching (rotation around an Z₂-axis), yawing(rotation around a Y₂-axis), a Y₂-axis direction, a Z₂-axis directionand an X₂-axis (optical axis) direction. However, in FIG. 1 and thefollowing description, an image stabilization system in the pitchingrotation and the Y₂-axis direction, and an optical axis direction imagestabilization system in the X₂-axis (optical axis) direction are shown,and an image stabilization system in the yawing rotation and the Z₂-axisdirection is assumed to be the same as the image stabilization system ofthe pitching rotation and the Y₂-axis direction.

An angular velocity sensor 130 is an angular velocity detector which isfloatingly supported with respect to the lens barrel 102, and detectsthe angular velocity of the movement which occurs to the camera body 201(lens barrel 102). The angular velocity sensor 130 according to theembodiment 1 is a piezoelectric vibration angular velocity sensor thatdetects Coriolis force which is generated by rotation. The angularvelocity sensor 130 is an angular velocity sensor internally havingsensitivity axes for three axis rotation of pitching, yawing androlling. The reason why the angular velocity sensor 130 is floatinglysupported is to eliminate the influence of mechanical vibrationaccompanying the mechanism operation of the camera as much as possible.The angular velocity sensor 130 outputs an angular velocity signalcorresponding to a detected angular velocity to a filter 160 c.

An accelerometer 121 is an acceleration detector that detects theacceleration of the movement which occurs to the camera body 201 (lensbarrel 102). The accelerometer 121 according to the embodiment 1 is atriaxial accelerometer having three sensitivity axes with respect to thethree directions, the X-axis, Y-axis and Z-axis, and is floatinglysupported by the lens barrel 102. The accelerometer 121 is floatinglysupported for the same reason as the case of the angular velocity sensor130. Further, the accelerometer 121 is a triaxial acceleration sensor(acceleration sensor using a weight) in the present embodiment, and thefrequency characteristics of two axes are equally high, but thecharacteristic of the remaining one axis is low. Therefore, in order todetect the accelerations in the Y₂-axis direction and the Z₂-axisdirection orthogonal to the optical axis, the two axes with highsensitivity are used, and the one axis low in characteristic is alignedwith the X₂-axis (optical axis direction). This is for preciselydetecting the accelerations in the Y₂-axis direction and the Z₂-axisdirection which have a large influence on image blur correction.

The output of the accelerometer 121 is A/D-converted after passingthrough a filter 160 a such as a low pass filter (LPF), and is input toan image stabilizing lens correction calculator 107 in a lens CPU 106.The accelerometer 121 may be mounted to a movable mirror frame whichmoves in the optical axis direction during zooming or the like, but insuch a case, it is necessary to enable the position of the accelerometer121 with respect to the principal point position after zooming to bedetected.

Further, the angular velocity sensor 130 is of a vibratory gyro type asdescribed above, and vibrates at about 26 KHz. Accordingly, if thesesensors are mounted on the same substrate, the accelerometer 121 islikely to pick up the vibration noise, and therefore, the accelerometer121 and angular velocity sensor 130 are mounted on separate substrates.

An image stabilizing lens driver 120 is a driver (actuator) whichgenerates a drive force for driving a correcting lens 101 for correctionof the image blur within the plane (within the Y₂Z₂ plane) perpendicularto an optical axis I. The image stabilizing lens driver 120 generates adrive force in the Y₂-axis direction, and drives the correcting lens 101when a coil not illustrated is brought into an energized state by thedrive current output by a voltage driver 161.

A lens position detector 110 is an optical position detector whichdetects the position of the correcting lens 101 in the planeperpendicular to the optical axis I. The lens position detector 110monitors the present position of the correcting lens 101, and feeds theinformation concerning the present position of the correcting lens 101to an image stabilizing controller 108 via an A/D converter.

The lens CPU 106 is a central processing unit that performs variouscontrols of the lens barrel 102 side. The lens CPU 106 calculates thefocal length based on the pulse signal output by a focal length detector163, and calculates an object distance based on the pulse signal outputby an object distance detector 164. Further, in the lens CPU 106, theimage stabilizing lens correction calculator 107, the image stabilizingcontroller 108 and an autofocus lens controller 401 are provided. Thelens CPU 106 can perform communication with a body CPU 109 via a lensjunction 190 provided between the lens barrel 102 and the camera body201. An image blur correction start command is sent from the body CPU109 synchronously with half depression ON of a release switch 191 and animage blur correction stop command is sent to the CPU 106 synchronouslywith half depression OFF.

Further, the lens CPU 106 monitors the state of a blur correction switch(SW) 103 provided in the lens barrel 102. If the blur correction switch103 is ON, the lens CPU 106 performs image blur correction control, andif the blur correction switch 103 is OFF, the lens CPU 106 ignores theimage blur correction start command from the body CPU 109 and does notperform blur correction.

The image stabilizing lens correction calculator 107 is a part whichconverts the output signals of the filters 160 a and 160 c into thetarget velocity information for driving the correcting lens 101 to thetarget position. The image stabilizing controller 108, the filters 160 aand 160 c, an EEPROM 162, the focal length detector 163 and the objectdistance detector 164 are connected to the image stabilizing lenscorrection calculator 107. The autofocus lens controller 401 has anoptical axis direction movement velocity calculator 402 which performscalculation for performing optical axis direction movement correction,by using the accelerometer output value from the image stabilizing lenscorrection calculator 107, and outputs the calculation result to anautofocus lens voltage driver 172.

An autofocus lens 140 can be driven in the optical axis direction by anautofocus lens driver 141 using an ultrasonic motor or a stepping motoras a drive source. The autofocus lens voltage driver 172 generates avoltage for performing drive control of the autofocus lens driver 141.

The image stabilizing lens correction calculator 107 captures the outputsignals (analog signals) output from the angular velocity sensor 130 andthe accelerometer 121 through the filters 160 a and 160 c by quantizingthe output signals by A/D conversion. Based on the focal lengthinformation obtained from the focal length detector 163, the objectdistance information obtained from the object distance detector 164 andthe information peculiar to the lens which is written in the EEPROM 162,the image stabilizing lens correction calculator 107 converts thesignals into the target drive velocity of the correcting lens 101. Theconversion method (calculating method) to the target drive positionperformed by the image stabilizing lens correction calculator 107 willbe described in detail later. The target velocity signal which is theinformation of the target drive velocity calculated by the imagestabilizing lens correction calculator 107 is output to the imagestabilizing controller 108.

The image stabilizing controller 108 is the part which controls theimage stabilizing lens driver 120 via the voltage driver 161, andperforms follow-up control so that the correcting lens 101 is driven asthe information of the target drive velocity. The image stabilizingcontroller 108 converts the position detection signal (analog signal)output by the lens position detector 110 into a digital signal andcaptures the digital signal. The input part to the image stabilizingcontroller 108 is for the target velocity signal converted into thetarget drive velocity of the correcting lens 101 which is the output ofthe image stabilizing lens correction calculator 107, and another inputpart is for the positional information of the correcting lens 101 whichis obtained by the lens position detector 110.

As the control in the image stabilizing controller 108, velocity controlis performed by using the deviation between the target drive velocity ofthe correcting lens 101 and the actual velocity information. The imagestabilizing controller 108 calculates a drive signal based on the targetdrive velocity, velocity information of the correcting lens 101 and thelike, and outputs the digital drive signal to the voltage driver 161.

Alternatively, as the control in the image stabilizing controller 108,known PID control may be used. PID control is performed by using thedeviation of the target positional information and the lens positionalinformation of the correcting lens 101. The image stabilizing controller108 calculates the drive signal based on the target positionalinformation, the positional information of the correcting lens 101 andthe like, and outputs the digital drive signal to the voltage driver161.

The filters 160 a and 160 c are filters which remove predeterminedfrequency components from the output signals of the angular velocitysensor 130 and the accelerometer 121, and cut the noise component andthe DC component included in the high-frequency band. The filters 160 aand 160 c perform A/D conversion of the angular velocity signals afterthe predetermined frequency components are removed, and thereafter,output the angular velocity signals to the image stabilizing lenscorrection calculator 107.

The voltage driver 161 is a driver which supplies power to the imagestabilizing driver 120 according to the input drive signal (drivevoltage). The voltage driver 161 performs switching for the drivesignal, applies a voltage to the image stabilizing lens driver 120 todrive the image stabilizing lens driver 120.

The EEPROM 162 is a nonvolatile memory which stores lens data that isvarious kinds of unique information concerning the lens barrel 102 andthe coefficients for converting the pulse signals output by the objectdistance detector 164 into physical quantities.

The focal length detector 163 is a zoom encoder which detects a focallength. The focal length detector 163 outputs the pulse signalcorresponding to a focal length value to the image stabilizing lenscorrection calculator 107. The object distance detector 164 is afocusing encoder for detecting the distance to an object. The objectdistance detector 164 detects the position of a shooting optical system105 (autofocus lens 140), and outputs the pulse signal corresponding tothe position to the image stabilizing lens correction calculator 107.

From the detection results of the focal length detector 163 and theobject distance detector 164, the position of the principal point A ofthe shooting optical system 105 is calculated as will be describedlater. Alternatively, the positional information of the principal pointA of the shooting optical system 105 stored in the EEPROM 162 is read,and control which will be described later is performed.

The body CPU 109 is a central processing unit which performs variouscontrols of the entire camera system. The body CPU 109 transmits a blurcorrection start command to the lens CPU 106 based on the ON operationof the release switch 191. Alternatively, the body CPU 109 transmits ablur correction stop command to the lens CPU 106 based on the OFFoperation of the release switch 191. Alternatively, the body CPU 109performs various other kinds of processing. Information on the releaseswitch 191 is input to the body CPU 109, and the release switch 191 candetect half depressing or fully depressing operation of the releasebutton not illustrated. The release switch 191 is a switch which detectsthe half depressing operation of the release button not illustrated,starts a series of shooting preparing operations, detects a fullydepressing operation of the release button and starts a shootingoperation.

Next, an interior of the image stabilizing lens correction calculator107 will be described in detail.

A rotation angular velocity calculator 301 calculates a rotation angularvelocity {dot over (θ)}_(caxy) based on the angular velocity sensoroutput. The angular velocity sensor output and the rotation angularvelocity are generally in the linear relation, and therefore, therotation angular velocity can be obtained by multiplying the angularvelocity sensor output by a coefficient.

An accelerometer output corrector 302 practically obtains only the valueof the third term (=jr_(axy){umlaut over (θ)}_(axy): revolution angularacceleration component) by performing erasure calculation of the fourthterm to the seventh term of expression (27) which will be describedlater based on an output value of accelerometer A_(ccy2(O-X2Y2)) and therotation angular velocity {dot over (θ)}_(caxy). A single dot onreference symbol represents the first derivative value and two dots onreference symbol represent the second derivative value with respect totime.

The fifth term and the sixth term of the unnecessary terms in expression(27) are the ones considering the position of the principal point A ofthe shooting optical system 105 and the position of the accelerometer121 which are described in the present invention, and by performingerasure calculation of the unnecessary terms considering the positions,accurate blur correction can be made. The details will be describedlater.

A high-pass filter 303 is a filter which transmits a frequency componentnecessary for blur correction. A revolution angular velocity calculator304 can obtain a revolution angular acceleration {umlaut over (θ)}_(axy)by dividing a revolution acceleration component jr_(axy){umlaut over(θ)}_(axy) which is the input value from the high-pass filter 303 by anobject side focal length r_(axy). Further, by performing timeintegration of the revolution angular acceleration, a revolution angularvelocity {dot over (θ)}_(axy) necessary for control is obtained.

A rotation revolution difference image stabilization amount calculator305 calculates the image movement velocity in the Y₂ direction of theimage pickup surface of the image pickup device 203 by substituting aread imaging magnification: β, an actual focal length value: f, and therotation angular velocity {dot over (θ)}_(caxy) and the revolutionangular velocity {dot over (θ)}_(axy), which are calculated in realtime, into the following Expression (15)which will be described later.

{right arrow over (V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎ ≈(1+β)f({dot over(θ)}_(caxy)−{dot over (θ)}_(axy))e^(j(π/2))   (15)

The obtained image movement velocity becomes the target drive velocity.The image movement velocity in the Z₂ direction of the image pickupsurface can be similarly obtained from expression (16) which will bedescribed later, but the description will be omitted here.

A theoretical formula selector 306 selects use of the formula ofrotation revolution difference movement correction using a differencebetween the rotation angular velocity and the revolution angularvelocity, or use of the formula of rotation movement correction usingonly a rotation angular velocity as the formula used for correctioncalculation, according to the ratio of the revolution angular velocityto the rotation angular velocity.

<<Meaning and Use Method of Rotation Revolution Blur Formula Expression(15)>>

In embodiment 1, the components of the camera shake (pitching anglemovement and parallel movement in the Y₂ direction) in the XY plane areexpressed by the rotation revolution movement formula, and the Y₂direction image movement in the image pickup surface (image pickupsurface vertical direction image movement) velocity is obtained byExpression (15) which is the approximate expression of the rotationrevolution movement formula. In the description of the presentinvention, “vector R” is described as “{right arrow over (R)}”.

{right arrow over (V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎≈−(1+β)f({dot over(θ)}_(caxy)−{dot over (θ)}_(axy))e^(j(π/2))   (15)

where {right arrow over (V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎ represents animage movement velocity vector in an image pickup surface, β representsan imaging magnification (without unit) at the time of image blurcorrection of the shooting lens of this camera, f represents an actualfocal length (mm) at the time of image blur correction of the shootinglens of this camera, (1+β)f represents an image side focal length (mm),{dot over (θ)}_(caxy) represents time derivative value of the rotationangle θ_(caxy) about the principal point A as the center, rotationangular velocity (rad/sec), {dot over (θ)}_(axy) represents timederivative value of the revolution angle θ_(axy) about an origin O asthe center, and the revolution angular velocity (rad/sec), ande^(j(π/2)) represents that the image movement velocity vector indicatesthe direction rotated by 90 degrees from the X₂-axis (optical axis) inthe polar coordinate system because of (π/2)^(th) power.

The detailed deriving procedure of the approximate theoretical formulaof the image movement velocity {right arrow over (V)}_(dcxy(O) ₂ _(-X) ₂_(Y) ₂ ₎ in the moving coordinate system O₂-X₂Y₂ in the XY plane whichis expression (15) will be described later, and here, the meaning ofthis formula will be described with reference to FIG. 2.

FIG. 2 shows a schematic diagram of a state of a camera which isprojected on an XY plane. Here, the outer shape and the lens of thecamera are illustrated. In the camera, a principal point A_(xy) of theoptical system, an accelerometer B_(xy), a center C_(xy) of the imagepickup device 203 are illustrated. An origin O₄ of the coordinate systemO₄-X₄Y₄ is fixed to a principal point A_(xy) of the optical system. Whenthe principal point A_(xy) is moved, an X₄-axis keeps a parallel statewith respect to the X-axis, and a Y₄-axis keeps the parallel state withrespect to a Y-axis. An origin O₂ of a coordinate system O₂-X₂Y₂ isfixed to the principal point A_(xy), and moves integrally with thecamera. In this case, the X₂-axis is always matched with the opticalaxis of this camera.

The angle around the origin O₂ from the X₄-axis to the X₂-axis is set asthe rotation angle θ_(caxy). The angle around the origin O from theX-axis to a scalar r_(axy) is set as a revolution angle θ_(axy). Scalarr_(axy)≈(1+β)f/β represents an object side focal length. β is an imagingmagnification. A gravity acceleration vector {right arrow over (G)}_(xy)at the principal point A_(xy) has an angle θ_(gxy) around the principalpoint A_(xy) from the X₄-axis to the {right arrow over (G)}_(xy) bynormal rotation (counterclockwise). The θ_(gxy) is a constant value.

The approximate expression means that the image movement velocity in theY₂ direction in the image pickup surface can be expressed by −(imageside focal length)×(value obtained by subtracting the revolution angularvelocity from the rotation angular velocity). The strict formula withoutapproximation is expression (12). When image blur correction with higherprecision is performed, the strict formula expression (12) may be used.Here, r_(axy)≈(1+β)f/β represents the object side focal length.

$\begin{matrix}\begin{matrix}{{\overset{arrow}{V}}_{d\; c\; x\; {y{({O_{2} - {X_{2}Y_{2}}})}}} = {{\lbrack {\frac{f{\overset{.}{r}}_{a\; x\; y}}{r_{a\; x\; y} - f} - \frac{f\; r_{a\; x\; y}{\overset{.}{r}}_{a\; x\; y}}{( {r_{a\; x\; y} - f} )^{2}}} \rbrack ^{j{({\theta_{a\; x\; y} - \theta_{c\; a\; x\; y}})}}} +}} \\{{{\frac{f{\overset{.}{r}}_{a\; x\; y}}{r_{a\; x\; y} - f}{\overset{.}{\theta}}_{a\; x\; y}^{j{(\begin{matrix}{\theta_{a\; x\; y} + \frac{\pi}{2} -} \\\theta_{c\; a\; x\; y}\end{matrix})}}} - {( {1 + \beta} )f\; {\overset{.}{\theta}}_{c\; a\; x\; y}^{j{(\frac{\pi}{2})}}}}}\end{matrix} & (12)\end{matrix}$

Similarly to the case of the XY plane, the components of the yawingangle movement of the camera shake on the ZX plane and the parallelmovement in the Z₂-direction are expressed by the rotation revolutionmovement formula, and the Z₂ direction image movement (image movement inthe lateral direction of the image pickup surface) velocity in the imagepickup device surface is obtained by the approximate expression (16).This means the same thing as expression (15) described above, andtherefore, the description will be omitted here.

Next, the component included in the output of the accelerometer 121 willbe described. The deriving procedure of the formula will be describedlater. Here, the necessary items for image stabilization will bedescribed. The accelerometer output A_(ccy2(O-X2Y2)) in the Y₂-axisdirection, which is used for obtaining the revolution angular velocity{dot over (θ)}_(axy) is represented by expression (27).

$\begin{matrix}{A_{c\; c\; {y_{2}{({O - {X_{2}Y_{2}}})}}} \approx {j\; r_{a\; x\; y}{\overset{¨}{\theta}}_{a\; x\; y}}} & {( {{third}\mspace{14mu} {term}\text{:}\mspace{14mu} {acceleration}\mspace{14mu} {of}\mspace{14mu} {revolution}} )} \\{{+ {j2}}{\overset{.}{r}}_{a\; x\; y}{\overset{.}{\theta}}_{a\; x\; y}} & {( {{fourth}\mspace{14mu} {term}\text{:}\mspace{14mu} {Coriolis}\mspace{14mu} {force}} )} \\{{+ j}\; r_{b\; a\; x\; y}{\overset{.}{\theta}}_{c\; a\; x\; y}^{2}{\sin ( {\theta_{b\; a\; x\; y} + \pi} )}} & {( {{fifth}\mspace{14mu} {term}\text{:}\mspace{14mu} {centripetal}\mspace{14mu} {force}\mspace{14mu} {of}\mspace{14mu} {rotation}} )} \\{{+ j}\; r_{b\; a\; x\; y}{\overset{¨}{\theta}}_{c\; a\; x\; y}{\sin ( {\theta_{b\; a\; x\; y} + \frac{\pi}{2}} )}} & {( {{sixth}\mspace{14mu} {term}\text{:}\mspace{14mu} {acceleration}\mspace{14mu} {of}\mspace{14mu} {rotation}} )} \\{j\; G\; {\sin ( {\theta_{g\; x\; y} - \pi} )}} & {( {{seventh}\mspace{14mu} {term}\text{:}\mspace{14mu} {gravity}\mspace{14mu} {acceleration}\mspace{14mu} {component}} )}\end{matrix}$

The third term jr_(axy){umlaut over (θ)}_(axy) in expression (27) is thecomponent necessary for obtaining the revolution angular velocity {dotover (θ)}_(axy) which is desired to be obtained in embodiment 1, and ifthe third term is divided by the known r_(axy), and is integrated, therevolution angular velocity {dot over (θ)}_(axy) is obtained. The fourthterm, the fifth term, the sixth term and the seventh term areunnecessary terms for calculation, and unless they are erased, theybecome the error components at the time of obtaining the revolutionangular velocity {dot over (θ)}_(axy). The fourth term j2{dot over(r)}_(axy){dot over (θ)}_(axy) represents Coriolis force, and if themovement in the camera optical axis direction is small, the velocity inthe optical axis direction {dot over (r)}_(axy)≈0, the fourth term isthe term which can be ignored. Expression (27) will be also describedlater.

The fifth term (the first correction component) and the sixth term (thesecond correction component) are error components which are included inthe accelerometer output A_(ccy2(O-x2y2)) since the accelerometer 121cannot be disposed in the ideal principal point position A, and isdisposed in the position B. The fifth term jr_(baxy){dot over(θ)}_(caxy) ² sin(θ_(baxy)+π) is the centripetal force which isgenerated due to the rotation of the accelerometer 121 around theprincipal point A. r_(baxy) and θ_(baxy) represent the coordinates ofthe position B where the accelerometer 121 is mounted, and are known.{dot over (θ)}_(caxy) represents a rotation angular velocity, and is thevalue which can be measured by the angular velocity sensor 130 mountedon the camera. Therefore, the value of the fifth term can be calculated.

The sixth term jr_(baxy){umlaut over (θ)}_(caxy) sin(θ_(baxy)+π/2) isthe acceleration component when the accelerometer 121 rotates around theprincipal point A, and r_(baxy) and θ_(baxy) represent the coordinatesof the position B where the accelerometer 121 is mounted, and are known.{umlaut over (θ)}_(caxy) can be calculated by differentiating the valueof the angular velocity sensor 130 mounted on the camera. Therefore, thevalue of the sixth term can be calculated.

The seventh term jG sin(θ_(gxy)−π) is the influence of the gravityacceleration, and can be dealt as a constant in this approximateexpression, and therefore, can be eliminated by the filtering processingof a circuit.

The accelerometer output A_(ccx2(O-X2Y2)) in the X₂-axis direction thatis an optical axis for use in optical axis direction movement correctionis represented by expression (26).

A_(ccx) ₂ _((O-X) ₂ _(Y) ₂ ₎≈{umlaut over (r)}_(axy) (first term:optical axis direction movement)

−r_(axy){dot over (θ)}_(axy) ² (second term: centripetal force ofrevolution)

+r_(baxy){dot over (θ)}_(caxy) ² cos(θ_(baxy)+π) (fifth term:centripetal force of rotation)

+r_(baxy){umlaut over (θ)}_(caxy) cos(θ_(baxy)+π/2) (sixth term:acceleration of rotation)

+G cos(θ_(gxy)−π) (seventh term: gravity acceleration component)   (26)

In expression (26), what is necessary for optical axis directionmovement correction is only the first term {umlaut over (r)}_(axy)(acceleration in the optical axis direction). The second term, the fifthterm, the sixth term and the seventh term are the components unnecessaryfor the optical axis direction movement correction, and unless they areerased, they become error components at the time of obtaining theacceleration {umlaut over (r)}_(axy) in the X₂-axis direction which isthe optical axis. The second term, the fifth term, the sixth term andthe seventh term can be erased by the similar method to the case ofexpression (27). Expression (26) will also be described later.

<<Description of Flowchart>>

FIG. 3 is comprised of FIGS. 3A and 3B showing flowcharts illustratingthe flow of the operation relating to the image stabilizing lenscorrection of the image stabilization apparatus in embodiment 1.Hereinafter, the operation relating to the correction amount calculationof the correcting lens 101 will be described according to FIGS. 3A and3B.

In step (hereinafter, described as S) 1010, when the blur correction SW103 is in an ON state, a correction start command is output from thecamera body 201 by half depression ON of the release switch 191. Byreceiving the correction start command, the blur correction operation isstarted.

In S1020, it is determined whether or not a blur correction stop commandis output from the camera body 201, and when it is output, the flowproceeds to S1400, and the blur correcting operation is stopped. When itis not output, the flow proceeds to S1030 to continue the blurcorrection operation. Accordingly, the blur correction operation iscontinued until a blur correction stop command is output from the camerabody 201.

In S1030, the numeric value obtained from the focal length detector 163is read. The numeric value of the focal length detector 163 is used forcalculation of the imaging magnification β. In S1040, the numeric value(absolute distance) obtained from the object distance detector 164 isread. In S1050, the imaging magnification β is calculated based on thenumeric value of the focal length detector 163 and the numeric value ofthe object distance detector 164. Calculation of the imagingmagnification β is a unique formula according to the optical systemconfiguration, and calculation is performed based on the imagingmagnification calculation formula. The obtaining of the imagingmagnification β does not especially have to be performed based on theformula, but the imaging magnification may be obtained from a table withrespect to the encoder position of the focal length and the absolutedistance.

In S1060, the outputs of the angular velocity sensor 130 and theaccelerometer 121 are read. In S1070, the rotation angular velocity {dotover (θ)}_(caxy) is calculated based on the angular velocity sensoroutput from S1310. The angular velocity sensor output and the rotationangular velocity are generally in the linear relation, and therefore,the rotation angular velocity can be obtained by multiplication by acoefficient.

In S1410, it is determined whether the release switch 191 is fullydepressed to be ON, that is, whether the release button not illustratedis fully depressed. If YES, that is, if it is the exposure time of thecamera, the flow proceeds to S1420, and if NO, that is, if it is beforeexposure, the flow proceeds to S1090. In S1090, by performing erasurecalculation of the fourth term to the seventh term of expression (27)based on the output value of accelerometer A_(ccy2(O-X2Y2)) from S1080and the rotation angular velocity {dot over (θ)}_(caxy) from S1070, andthereby, substantially only the value of the third term: jr_(axy){umlautover (θ)}_(axy) is obtained.

More specifically, for example, in the output of accelerometerA_(ccy2(O-X2Y2)) in the Y₂-axis direction, the values of the fifth termand the sixth term are calculated by performing calculation of r_(baxy)and θ_(baxy) which are the relative positional information of theposition of the principal point A of the shooting optical system 105with respect to the accelerometer 121 based on the principal pointposition information of S1050, and the values of the fifth term and thesixth term are removed from the output A_(ccy2(O-X2Y2)). The fourth termand the seventh term are as described above.

In S1100, the output value of S1090: jr_(axy){umlaut over (θ)}_(axy) isdivided by the object side focal length r_(axy), and thereby, therevolution angular acceleration {umlaut over (θ)}_(axy) is obtained.

Further, by performing time integration of the revolution angularacceleration, the revolution angular velocity {dot over (θ)}_(axy)necessary for control is obtained. In the next S1104, the ratio of therevolution angular velocity to the rotation angular velocity obtained inS1070 is calculated. In the next S1106, the value of the rotationrevolution angular velocity ratio calculated in S1104 is stored. Whenthe previous value remains, the new one is written over the previousvalue and is stored, and the flow proceeds to S1110.

In S1420, the value of the rotation revolution angular velocity ratiostored in S1106 in the past is read, and the flow proceeds to 51110. In51110, it is determined whether or not the ratio of the rotation angularvelocity {dot over (θ)}_(caxy) from S1070 and the revolution angularvelocity {dot over (θ)}_(axy) from S1100 is larger than 0.1 (thepredetermined value). When the ratio is larger than 0.1 (thepredetermined value), the flow proceeds to S1120. When the ratio is 0.1(the predetermined value or less, the flow proceeds to S1130.

In the rotation revolution difference movement correction calculation ofS1120, the image movement velocity in the Y₂ direction of the imagepickup surface is calculated by substituting the read imagingmagnification β, the actual focal length value f, the rotation angularvelocity value {dot over (θ)}_(caxy) calculated in real time, and theestimated revolution angular velocity {dot over (θ)}_(axy) obtained bymultiplying the rotation revolution angular velocity ratio stored inS1106 by the rotation angular velocity value {dot over (θ)}_(caxy)calculated in real time into expression (15).

{right arrow over (V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎ ≈(1+β)f({dot over(θ)}_(caxy)−{dot over (θ)}_(axy))e^(j(π/2))   (15)

The obtained image movement velocity becomes the correction targetvelocity. The image movement velocity in the Z₂-direction of the imagepickup surface is similarly obtained from expression (16), but thedescription is omitted here.

In rotation movement correction calculation of S1130, the revolutionangular velocity {dot over (θ)}_(axy) which is substituted intoexpression (15) is set to be a constant, zero, without performingcalculation from the sensor output. Therefore, expression (15) issimplified, and written as follows.

{right arrow over (V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎ ≈−(1+β)f{dot over(θ)}_(caxy)e^(j(π/2))

If the rotation angular velocity {dot over (θ)}_(caxy) from S1070 inreal time is substituted into expression (15), the image movementvelocity in the Y₂-direction in real time is obtained.

In S1140, follow-up control calculation for driving the correcting lens101 is performed, with the sensitivity of the correcting lens 101 basedon taken into consideration, the image movement velocity obtained by therotation revolution difference movement correction calculation (S1120)or the rotation movement correction calculation (S1130). At this time,the present position output of the correcting lens 101 is simultaneouslymonitored.

In S1150, the calculation result is output to the voltage driver 161which drives the correcting lens 101 based on the follow-up controlcalculation result in S1140. After the calculation result is output tothe voltage driver 161, the flow returns to S1020.

In S1300, it is determined whether or not the imaging magnification β is0.15 or more. When the imaging magnification β is 0.15 or more, the flowproceeds to S1320. When the imaging magnification β is less than 0.15 inS1300, the flow proceeds to S1410.

In S1320, the unnecessary terms (the second, fifth, sixth and seventhterms) of expression (26) are calculated and erased based on the angularvelocity sensor output A_(ccx2(O-X2Y2)) in the X₂-axis (optical axis)direction from S1310 and the rotation angular velocity {dot over(θ)}_(caxy) from S1070, and the first term {umlaut over (r)}×_(axy),which is an necessary acceleration in the optical axis direction, iscalculated. By time integration of the first term, the optical axisdirection movement velocity {dot over (r)}_(axy) is obtained.

In S1330, based on the optical axis direction blur velocity {dot over(r)}_(axy) from S1320, follow-up control calculation for driving theautofocus lens 140 is performed. In S1340, based on the follow-upcontrol calculation result in S1330, the calculation result is output tothe autofocus lens voltage driver 172 which drives the autofocus lens140, and thereafter, the flow returns to S1020.

In the above description, in S1090, based on the principal pointposition information from S1050, the output value of accelerometerA_(ccy2(O-X2Y2)) from S1080 and the rotation angular velocity {dot over(θ)}_(caxy) from S1070, for example, in the output of accelerometerA_(ccy2(O-X2Y2)) in the Y₂-axis direction, the values of the fifth termand the sixth term are calculated by performing calculation of r_(baxy)and θ_(baxy) which are the relative position information between theposition of the principal point A of the shooting optical system 105 andthe accelerometer 121 from the principal point position information ofS1050, and the values of the fifth term and the sixth term are removedfrom the output A_(ccy2(O-X2Y2)), but the control as follows may beadopted. It goes without saying that, for example, the values ofr_(baxy) and θ_(baxy) corresponding to the calculation value of theimaging magnification β of S1050 are written in the EEPROM 162, and byreading them in S1090, the values of the fifth term and the sixth termmay be calculated, or the similar effect also can be obtained if thecalculation formulae of the fifth term and the sixth term correspondingto the calculated value of the imaging magnification β are written inthe EEPROM 162, and by reading them in S1090, the values of the fifthterm and the sixth term are calculated based on the rotation angularvelocity {dot over (θ)}_(caxy) from S1070.

<<Detailed Description of Rotation Revolution Model Diagram and RotationRevolution Movement Formula>>

Hereinafter, description of a rotation revolution model diagram anddescription of a rotation revolution movement formula will be performed.First, the coordinate system of the image stabilization apparatus willbe described.

First, a moving coordinate system O₂-X₂Y₂Z₂ which is fixed onto thecamera will be described. At the time of camera being shaken, thecoordinate system O₂-X₂Y₂Z₂ performs shake movement integrally with thecamera, and therefore, the coordinate system is called a movingcoordinate system.

A three-dimensional coordinate system will be described with athree-dimensional coordinate system diagram of FIG. 4A. The coordinatesystem is an orthogonal coordinate system, and as in FIG. 4A, theX₂-axis, Y₂-axis and Z₂-axis are orthogonal to one another. Pitching isdefined as the rotation about the Z₂-axis around the origin O₂ and thepitching from the +X₂-axis to the +Y₂-axis is assigned with plus signwith the origin O₂ as the center. Yawing is defined as the rotationabout the Y₂-axis around the origin O₂ and the yawing from the +Z₂-axisto the +X₂-axis is assigned with plus sign. Rolling is defined as therotation about the X₂-axis around the origin O₂ and the rolling from the+Y₂-axis to the +Z₂-axis is assigned with plus sign.

FIG. 4D is a camera side view with the camera sectional view of FIG. 1being simplified, and the lens is illustrated in the see-through state.With the camera side view of FIG. 4D, the coordinate system O₂-X₂Y₂Z₂which is fixed to the camera will be described.

The origin O₂ of the coordinate system is fixed to the principal point Aof the entire optical system (shooting optical system 105) which existsin the lens barrel 102, and the image pickup device direction on theoptical axis is set as the plus direction of X₂-axis. The camera upperdirection (upper direction of this drawing) is set as the plus directionof Y₂-axis, and the remaining direction is set as the plus Z₂-axis. Inthe state in which the camera is projected on an X₂Y₂ plane, a positionB of the accelerometer 121 is expressed by a line segment lengthr_(baxy) between the origin O₂ and the position B of the accelerometer121, and an angle θ_(baxy) formed by the X₂-axis and the line segmentr_(baxy). The rotational direction in the direction to the plus Y₂-axisfrom the plus X₂-axis with the O₂-axis as the center is set as plusdirection.

The camera top view of FIG. 4B illustrates the position B of theaccelerometer 121 in the state projected onto a Z₂X₂ plane. In the statein which the camera is projected onto the Z₂X₂ plane, the position B ofthe accelerometer 121 is expressed by a line segment length r_(bazx)between the origin O₂ and the position B of the accelerometer 121 and anangle ψ_(bazx) formed by the Z₂-axis and the line segment r_(bazx). Therotational direction in the direction to +X₂-axis from the +Z₂-axis isset as plus direction. Further, the position B is also expressed by anangle ζ_(bazx) formed by the X₂-axis and the line segment r_(bazx). Therotational direction in the direction to the +Z₂-axis from the +X₂-axisis set as plus direction.

The camera front view of FIG. 4C illustrates the position of theaccelerometer 121 in the state projected onto a Y₂Z₂ plane. In the stateprojected onto the Y₂Z₂ plane, the position B of the accelerometer 121is expressed by a line segment length r_(bayz) between the origin O₂ andthe position B of the accelerometer 121, and an angle ρ_(bayz) formedbetween the Y₂-axis and the line segment r_(bayz). The rotationaldirection in the direction to the +Z₂-axis from the +Y₂-axis with theO₂-axis as the center is set as plus direction.

Next, a fixed coordinate system O₉-X₉Y₉Z₉ where an object S is presentwill be described. The coordinate system O₉-X₉Y₉Z₉ is integral with theobject, and therefore, will be called a fixed coordinate system.

FIG. 5 is a diagram expressing only the optical system of the camera ina three-dimensional space. A point A=O₂ is the principal point A of theshooting optical system 105 already described, and is also an origin O₄of the coordinate system O₄-X₄Y₄Z₄.

The disposition of the initial state (time t=0) of the fixed coordinatesystem O₉-X₉Y₉Z₉ will be described. A coordinate origin O₉ is matchedwith the object to be shot. A coordinate axis +Y₉ is set in thedirection opposite to the gravity acceleration direction of the earth.The remaining coordinate axes +X₉ and +Z₉ are arbitrarily disposed. Apoint D is an imaging point of the object S, and is geometric-opticallypresent on the extension of a line segment OA.

With FIG. 6A, a three-dimensional expression method of the principalpoint A in the fixed coordinate system O₉-X₉Y₉Z₉ will be described.Since the position of the camera is illustrated on the space, only theprincipal point A to be the reference is illustrated in FIG. 6A, and theother portions such as the imaging point D are not illustrated. Theprincipal point A is shown by the vector with the origin O₉ as thereference, and is set as {right arrow over (R)}_(a). The length of the{right arrow over (R)}_(a) is set as a scalar r_(a). An angle to the{right arrow over (R)}_(a) from the Z₉-axis with O₉ as the center is setas ψ_(a). An angle from the X₉-axis to a straight line OJ, which is theline of intersection between a plane including the {right arrow over(R)}_(a) and the Z₉-axis and the XY plane, is set as θ_(a).

As described above, {right arrow over (R)}_(a) can be expressed in thepolar coordinate system by three values of the scalar r_(a), the angleψ_(a) and the angle θ_(a). If the three values can be calculated frommeasurement by a sensor and the like, the position of the principalpoint A of the camera is obtained.

<<Reference: Orthogonal Coordinate System Transformation Formula>>

In this case, the formula for transforming the position of the principalpoint A into an orthogonal coordinate system from a polar coordinatesystem is the following formula. In FIG. 6B, the orthogonal coordinatesystem is illustrated.

X _(a) =r _(a) sin ψ_(a)×cos θ_(a)

Y _(a) =r _(a) sin ψ_(a)×sin θ_(a)

Z_(a)=r_(a) cos ψ_(a)

(Description of Projection Coordinate System)

Next, the coordinate expression when the {right arrow over (R)}_(a) isprojected onto the X₉Y₉ plane and the coordinate expression when {rightarrow over (R)}_(a) is projected onto the Z₉X₉ plane will be describedwith reference to FIG. 7. With FIG. 7, a moving coordinate systemO₄-X₄Y₄Z₄ will be described. The moving coordinate system O₄-X₄Y₄Z₄ isalso provided to the principal point A. An origin O₄ is fixed to theprincipal point A. More specifically, the origin O₄ also moves withmovement of the principal point A. A coordinate axis +X₄ is alwaysdisposed to be parallel with the coordinate axis +X₉, and a coordinateaxis +Y₄ is always disposed parallel with the coordinate axis +Y₉. Theparallelism is also kept when the principal point A is moved. Thedirection of the gravity acceleration {right arrow over (G)} at theprincipal point A is a minus direction of the coordinate axis Y₉.

Two-dimensional coordinate expression when the camera is projected onthe X₉Y₉ plane will be described. In FIG. 7, the point where theprincipal point A is projected onto the X₉Y₉ plane is set as a principalpoint A_(xy). The line segment between the origin O₉ and the principalpoint A_(xy) is set as the scalar r_(axy), and the angle to the scalarr_(axy) from the X₉-axis with the origin O₉ as the center is set asθ_(axy). The angle θ_(axy) is the same angle as θ_(a) described above.In order to clarify the fact that this is projection onto the X₉Y₉plane, reference characters xy are assigned.

FIG. 8 illustrates the camera state projected on the X₉Y₉ plane. In thiscase, the outer shape and the lens of the camera are also illustrated.The origin O₄ of the coordinate system O₄-X₄Y₄ is fixed to the principalpoint A_(xy) which is described above. When the principal point A_(xy)is moved, the X₄-axis keeps a parallel state with the X₉-axis, and theY₄-axis keeps a parallel state with the Y₉-axis.

As described above, the origin O₂ of the coordinate system O₂-X₂Y₂ isfixed to the principal point A_(xy), and moves integrally with thecamera. At this time, the X₂-axis is always matched with the opticalaxis of this camera. The angle at the time of being rotated to theX₂-axis from the X₄-axis with the origin O₂ as the center is set asθ_(caxy) (=θ_(ca): completely the same value). The gravity acceleration{right arrow over (G)}_(xy) at the principal point A_(xy) has an angleθ_(gxy) from the X₄-axis in the positive rotation (counterclockwise) tothe {right arrow over (G)}_(xy) with the principal point A_(xy) as thecenter. The θ_(gxy) is a constant value.

Here, the terms used in the present invention will be described. In thepresent invention, by being likened to the movement of the sun and theearth, the origin O₉ where the object is present is compared to the sun,and the principal point A of the camera is compared to the center of theearth. The angle θ_(axy) is called “the revolution angle” within the XYplane, and the angle θ_(caxy) is called “the rotation angle” within theXY plane. More specifically, this is similar to the fact that revolutionindicates that the earth (camera) goes around the sun (object), whereasrotation indicates the earth (camera) itself rotates.

Next, two-dimensional coordinate expression when the camera is projectedonto the Z₉X₉ plane will be described. FIG. 9 illustrates the camerastate projected onto the Z₉X₉ plane. Here, the outer shape and the lensof the camera are also illustrated. The origin O₄ of the coordinatesystem O₄-Z₄X₄ is fixed to the principal point A_(zx). When theprincipal point A_(zx) is moved, the Z₄-axis keeps a parallel state withthe Z₉-axis, and the X₄-axis keeps a parallel state with the X₉-axis.

The origin O₂ of the coordinate system O₂-Z₂X₂ is fixed to the principalpoint A_(zx), and moves integrally with the camera. At this time, theX₂-axis is always matched with the optical axis of the camera. The angleat the time of being rotated to the X₂-axis from the Z₄-axis with theorigin O₂ as the center is set as ψ_(cazx). Further, the angle at thetime of being rotated to the X₂-axis from the X₄-axis with the origin O₂as the center is set as ζ_(cazx).

In the three-dimensional coordinate system of FIG. 10, a camera initialstate at an initial time of a time t=0 will be described. Thedescription will be made on the assumption that in the fixed coordinatesystem O₉-X₉Y₉Z₉, a photographer causes the object S(t=0) desired to beshot to correspond to the center of the finder or the liquid crystaldisplay (LCD), and the object S(t=0) is on the optical axis forconvenience in this case. The origin O₉ is caused to correspond to theobject S(t=0). The principal point A of the shooting optical system 105and the imaging point D where the image of the object S(t=0) is formedare geometrically present on the optical axis of a straight line. Thegravity acceleration G at the position of the principal point A is inthe minus direction of the coordinate axis Y₉.

If the photographer causes the object S desired to be shot to correspondto the autofocus (AF) frame other than the center of the finder or theliquid crystal display (LCD), the line segment connecting the object Sand the principal point A is set as a {right arrow over (R)}_(a), andmay be modeled.

Next, a new fixed coordinate system O-XYZ is set. The origin O of thefixed coordinate system O-XYZ is caused to correspond to the origin O₉,and the coordinate axis X is caused to correspond to the optical axis ofthe camera. The direction of the coordinate axis Y is set so that thecoordinate axis Y₉ is present within the XY plane. If the coordinateaxis X and the coordinate axis Y are set, the coordinate axis Z isuniquely set.

As illustrated in FIG. 11, for convenience of description, the fixedcoordinate system O₉-X₉Y₉Z₉ will not be illustrated, and only the fixedcoordinate system O-XYZ will be illustrated as the fixed coordinatesystem hereinafter. By the aforementioned definition of the coordinatesystem, in the initial state at the time t=0, the gravity acceleration{right arrow over (G)} is present within the XY plane.

Next, the movement expression showing the relationship of the camerashake and image movement will be derived. In order to facilitateexpression of the mathematical expression, polar coordinate systemexpression is used. Further, the first order derivative and the secondorder derivative of the vector and the angle are performed. Thus, byusing FIG. 12 which is a basic explanatory diagram of a polar coordinatesystem, the meaning of the codes in the mathematical expression which iscommon and used here will be described. The positional expression of thepoint A which is present on the coordinate system O-XY is shown by aposition {right arrow over (R)}. The position {right arrow over (R)} isthe function of a time, and can be also described as {right arrow over(R)}(t).

Position Vector:

$\begin{matrix}\begin{matrix}{{\overset{arrow}{R}(t)} = {{r(t)}^{{j\theta}{(t)}}}} \\{= \overset{arrow}{R}} \\{= {r\; ^{j\theta}}} \\{= {{r\; \cos \; \theta} + {j\; r\; \sin \; \theta}}}\end{matrix} & (1)\end{matrix}$

The real term r cos θ is the X direction component, and the imaginaryterm jr sin θ is the Y direction component. Expressed in the orthogonalcoordinate system, the X direction component is A_(x)=r cos θ, and the Ydirection component is A_(y)=r sin θ.

Next, the velocity {right arrow over (V)}={dot over ({right arrow over(R)} is obtained by first order derivative of the position {right arrowover (R)} by the time t.

Velocity Vector:

$\begin{matrix}\begin{matrix}{\overset{arrow}{V} = \overset{arrow}{\overset{.}{R}}} \\{= {{\overset{.}{r}^{j\theta}} + {r\overset{.}{\theta}^{j{({\theta + \frac{\pi}{2}})}}}}}\end{matrix} & (2)\end{matrix}$

Expressed in the orthogonal coordinate system, the X direction componentis

V _(x)={dot over (A)}_(x)={dot over (r)} cos θ+r{dot over (θ)}cos(θ+π/2),

and the Y direction component is

V _(y)={dot over (A)}_(y)={dot over (r)} sin θ+r{dot over (θ)}sin(θ+π/2).

Next, the acceleration {umlaut over ({right arrow over (R)} is obtainedby the first order derivative of the velocity {dot over ({right arrowover (R)} by the time t.

Acceleration Vector:

{umlaut over (R)}={umlaut over (r)}e ^(jθ) +r{dot over (θ)} ² e^(j(θ+π)) +r{umlaut over (θ)}e ^(j(θ+π/2))+2{dot over (r)}{dot over(θ)}e ^(j(θ+π/2))   (3)

where the first term {umlaut over (r)}e^(jθ) represents the accelerationcomponent of a change in the length r, the second term r{dot over(θ)}²e^(j(θ+π)) represents the centripetal force component, the thirdterm r{umlaut over (θ)}e^(j(θ+π/2)) represents the angular accelerationcomponent, and the fourth term: 2{dot over (r)}{dot over(θ)}e^(j(θ+π/2)) represents the Coriolis force component.

Expressed in the orthogonal coordinate system, the acceleration vectoris obtained by the following expressions (4a) and (4b).

X Direction Component Ä_(x):

Ä_(x)={umlaut over (r)} cos θ+r{dot over (θ)} ² cos(θ+π)+r{umlaut over(θ)} cos(θ+π/2)+2{dot over (r)}{dot over (θ)} cos(θ+π/2)   (4a)

Y Direction Component Ä_(y):

Ä_(y)={umlaut over (r)} sin θ+r{dot over (θ)}² sin(θ+π)+r{umlaut over(θ)} sin(θ+π/2)+2{dot over (r)}{dot over (θ)} sin(θ+π/2)   (4b)

The theoretical formula of the present invention will be described inthe two-dimensional XY coordinate system when the camera is projectedonto the XY plane illustrated in FIG. 13. In FIG. 13, setting of thecoordinate system and codes of the two-dimensional XY coordinate systemwill be also described. Description will be made by partially includingthe content which is already described.

The object S is disposed on the fixed coordinate system O-XY. In theinitial state drawing at a time t=0, the codes will be described. In theinitial state (t=0), the optical axis of the camera corresponds to thecoordinate axis X of the fixed coordinate system O-XY. In the initialstate (t=0), the object S corresponds to the origin O of the fixedcoordinate system O-XY. In the fixed coordinate system O-XY, theprincipal point A is expressed by the {right arrow over (R)}_(axy). Theline segment length between the origin O and the principal point A ofthe camera is set as the scalar r_(axy), and the point where the originO forms an image by the lens is set as an image forming point D. A pointC is a center point of the image pickup device 203, and in the initialstate (t=0), the imaging point D corresponds to the point C.

In the moving state diagram at a certain time (t=t2), the codes will bedescried. The origin O₄ of the coordinate system O₄-X₄Y₄ is fixed to theprincipal point A, the coordinate axis X₄ is always kept parallel withthe coordinate axis X, and the coordinate axis Y₄ is always keptparallel with the coordinate axis Y. The origin O₂ of the coordinatesystem O₂-X₂Y₂ is fixed to the principal point A, and the coordinateaxis X₂ is always kept in the optical axis direction of the camera.

The accelerometer 121 is fixed to the point B inside the camera, and isexpressed by {right arrow over (R)}_(baxy) in the coordinate systemO₂-X₂Y₂. The length of a line segment AB 10065779US01 is set as thescalar r_(baxy), and the angle rotated to the line segment AB from thecoordinate axis X₂-axis with the origin O₂ as the center is set asθ_(baxy).

The image of the origin O forms an image at the position of a point Ddiffering from the point C of the image pickup device center by thelens. The imaging point D with the principal point A as the reference isexpressed by {right arrow over (R)}_(daxy). The point D with the point Cas the reference is expressed by {right arrow over (R)}_(dcxy). A scalarr_(dxxy) which is the length from the point C to the point D is thelength by which the image forming point D moves from the time t=0 to t2.The relative moving velocity vector of the image forming point D withrespect to the point C in the moving coordinate system O₂-X₂Y₂ at acertain time t2 is set as {right arrow over (V)}_(dcxy(O) ₂ _(-X) ₂ _(Y)₂ ₎.

In the fixed coordinate system O-XY, the angle formed to the {rightarrow over (R)}_(axy) from the coordinate axis X with the origin O asthe center is set as a rotation angle θ_(axy). In the moving coordinatesystem O₄-X₄Y₄, the angle formed from the coordinate axis X₄ to thecoordinate axis X₂ with the origin O₄ as the center is set as arevolution angle θ_(caxy).

The first order derivative of the {right arrow over (R)}_(axy) by thetime t is described as {dot over ({right arrow over (R)}_(axy), and thesecond order derivative of the (vector)R_(axy) by the time t isdescribed as {umlaut over ({right arrow over (R)}_(axy). The {rightarrow over (R)}_(caxy) is similarly described as {dot over ({right arrowover (R)}_(caxy) and {umlaut over ({right arrow over (R)}_(caxy), the{right arrow over (R)}_(daxy) is similarly described as a {dot over({right arrow over (R)}_(daxy) and {umlaut over ({right arrow over(R)}_(daxy), the revolution angle θ_(axy) is similarly described as {dotover (θ)}_(axy) and {umlaut over (θ)}_(axy), and the rotation angleθ_(caxy) similarly described as {dot over (θ)}_(caxy) and {umlaut over(θ)}_(caxy).

At a certain time t2, a relative moving velocity {right arrow over(V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎ of the imaging point D with the point Cas the reference in the moving coordinate system O₂-X₂Y₂ is obtained. Amoving velocity {right arrow over (V)}_(daxy(O-XY)) at the imaging pointD in the fixed coordinate system O-XY is obtained by the followingexpression (5).

$\begin{matrix}\begin{matrix}{{\overset{arrow}{V}}_{{daxy}{({O - {XY}})}} = {\overset{arrow}{\overset{.}{R}}}_{{daxy}{({O - {XY}})}}} \\{= {{{\overset{.}{r}}_{daxy}^{{j\theta}_{axy}}} + {r_{daxy}{\overset{.}{\theta}}_{daxy}^{j{({\theta_{axy} + \frac{\pi}{2}})}}}}} \\{= {{{\overset{.}{r}}_{daxy}^{{j\theta}_{axy}}} + {r_{daxy}{\overset{.}{\theta}}_{axy}^{j{({\theta_{axy} + \frac{\pi}{2}})}}}}} \\{{\because{\overset{.}{\theta}}_{daxy}} = {\overset{.}{\theta}}_{axy}}\end{matrix} & (5)\end{matrix}$

The moving velocity {right arrow over (V)}_(caxy(O-XY)) of the imagepickup device center C in the fixed coordinate system O-XY is obtainedby the following expression (6).

$\begin{matrix}{{\begin{matrix}{{\overset{arrow}{V}}_{{caxy}{({O - {XY}})}} = {\overset{\overset{arrow}{.}}{R}}_{{caxy}{({O - {XY}})}}} \\{= {{{\overset{.}{r}}_{caxy}^{{j\theta}_{caxy}}} + {r_{caxy}{\overset{.}{\theta}}_{caxy}^{j{({\theta_{caxy} + \frac{\pi}{2}})}}}}} \\{= {r_{caxy}{\overset{.}{\theta}}_{caxy}^{j{({\theta_{caxy} + \frac{\pi}{2}})}}}}\end{matrix}\because {\overset{.}{r}}_{caxy}} = 0} & (6)\end{matrix}$

Expression (7) is derived from the image formation formula ofgeometrical optics,

1/f=1/r _(axy)+1/r _(daxy)   (7),

where f represents focal length of the optical system. Expression (7) ismodified to obtain the following expression.

$r_{daxy} = \frac{{fr}_{axy}}{r_{axy} - f}$${\overset{.}{r}}_{daxy} = {f{{\overset{.}{r}}_{axy}( {r_{axy} - f} )}^{- 1}{fr}_{axy}{{\overset{.}{r}}_{axy}( {r_{axy} - f} )}^{- 2}}$

From the above expression, the relative moving velocity {right arrowover (V)}_(dcxy(O-XY)) of the imaging point D with respect to the pointC in the fixed coordinate system O-XY is obtained from the followingexpression (8).

$\begin{matrix}\begin{matrix}{{\overset{arrow}{V}}_{dcxy} = {\overset{\overset{arrow}{.}}{R}}_{dcxy}} \\{= {{\overset{arrow}{V}}_{dxy} - {\overset{arrow}{V}}_{cxy}}} \\{= {( {{\overset{arrow}{V}}_{daxy} - {\overset{arrow}{V}}_{axy}} ) - ( {{\overset{arrow}{V}}_{caxy} + {\overset{arrow}{V}}_{axy}} )}} \\{= {{\overset{arrow}{V}}_{daxy} - {\overset{arrow}{V}}_{caxy}}} \\{= {{{\overset{.}{r}}_{daxy}^{{j\theta}_{axy}}} + {r_{daxy}{\overset{.}{\theta}}_{axy}^{j{({\theta_{axy} + \frac{\pi}{2}})}}} - {r_{caxy}{\overset{.}{\theta}}_{caxy}^{j{({\theta_{caxy} + \frac{\pi}{2}})}}}}} \\{= {{\lbrack {{f{{\overset{.}{r}}_{axy}( {r_{axy} - f} )}^{- 1}} - {{fr}_{axy}{{\overset{.}{r}}_{axy}( {r_{axy} - f} )}^{- 2}}} \rbrack ^{{j\theta}_{axy}}} +}} \\{{{{{fr}_{axy}( {r_{axy} - f} )}^{- 1}{\overset{.}{\theta}}_{axy}^{j{({\theta_{axy} + \frac{\pi}{2}})}}} - {r_{caxy}{\overset{.}{\theta}}_{caxy}^{j{({\theta_{caxy} + \frac{\pi}{2}})}}}}}\end{matrix} & (8)\end{matrix}$

The relationship between the scalar r_(caxy) and the scalar r_(axy(t=0))is obtained from the following expression (9).

$\begin{matrix}\begin{matrix}{r_{caxy} = r_{{daxy}{({t = 0})}}} \\{= {f \cdot {r_{axy}( {t = 0} )} \cdot ( {r_{{axy}{({t = 0})}} - f} )^{- 1}}} \\{= {( {1 + \beta} )f}}\end{matrix} & (9)\end{matrix}$

By substituting the above described expression, the relative movingvelocity {right arrow over (V)}_(dcxy(O-XY)) in the fixed coordinatesystem O-XY is obtained by the following expression (10).

{right arrow over (V)} _(dcxy(O-XY)) =[f{dot over (r)} _(axy)(r _(axy)−f)⁻¹ −fr _(axy) {dot over (r)} _(axy)(r _(axy) −f)^('12) ]e ^(jθ)^(axy) +fr _(axy)(r _(axy) −f)⁻¹{dot over (θ)}_(axy) e ^(j(θ) ^(axy)^(+π/2))−(1+β)f{dot over (θ)} _(caxy) e ^(j(θ) ^(caxy) ^(+π/2))   (10)

Next, the coordinate is converted from the fixed coordinate system O-XYinto the moving coordinate system O₂-X₂Y₂ fixed onto the camera. Forthis, the {right arrow over (V)}_(dcxy(O-XY)) is rotated by the rotationangle (−θ_(caxy)). Therefore, the image movement velocity {right arrowover (V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎ in the moving coordinate systemO₂-X₂Y₂ fixed onto the camera is obtained from the following expression(11).

$\begin{matrix}\begin{matrix}{{\overset{arrow}{V}}_{{dcxy}{({O_{2} - {X_{2}Y_{2}}})}} = {{\overset{arrow}{V}}_{{dcxy}{({O_{2} - {X_{2}Y_{2}}})}}^{j{({- \theta_{caxy}})}}}} \\{= {{\begin{bmatrix}{{f{{\overset{.}{r}}_{axy}( {r_{axy} - f} )}^{- 1}} -} \\{{fr}_{axy}{{\overset{.}{r}}_{axy}( {r_{axy} - f} )}^{- 2}}\end{bmatrix}^{j{({\theta_{axy} - \theta_{caxy}})}}} +}} \\{{{{{fr}_{axy}( {r_{axy} - f} )}^{- 1}{\overset{.}{\theta}}_{axy}^{j{({\theta_{axy} + \frac{\pi}{2} - \theta_{caxy}})}}} -}} \\{{( {1 + \beta} )f{\overset{.}{\theta}}_{caxy}^{j{({\theta_{caxy} + \frac{\pi}{2} - \theta_{caxy}})}}}}\end{matrix} & (11)\end{matrix}$

When the expression is further organized, the aforementioned expression(12) is obtained. Since the image movement velocity {right arrow over(V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎ in the moving coordinate system O₂-X₂Y₂is the relative image movement velocity with respect to the image pickupsurface of the camera, the expression is a strict expression strictlyexpressing the movement of the image which is actually recorded as animage. In this strict expression, the imaginary part, namely, thecoordinate axis Y₂ direction component is the image movement componentin the vertical direction of the camera within the image pickup surface.Further, the real part of expression (12), namely, the coordinate axisX₂ direction component is the image movement component in the opticalaxis direction of the camera, and is a component by which a so-calledblurred image occurs.

The shake of the camera supported by the hand of a photographer isconsidered to be a vibration movement with very small amplitude with acertain point in the space as the center, and therefore, the imagemovement velocity {right arrow over (V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎ inthe moving coordinate system O₂-X₂Y₂ which is strictly obtained istransformed into an approximate expression under the followingconditions.

The state at the certain time t2 is assumed to be the vibration in thevicinity of the initial state at the time t=0, and the followingexpression (13) is obtained.

r_(axy)≈(1+β)f/β  (13)

When transformed, obtaining

r_(axy)−f≈f/β.

∵f·r _(axy)/(r _(axy) −f)=f·(1+β)(f/β)/(f/β)=f·(1+β).

If {dot over (r)}_(axy)≈0 and θ_(axy)+π/2−θ_(caxy)≈π/2 are substitutedinto {right arrow over (V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎, the followingexpression (14) is derived.

$\begin{matrix}\begin{matrix}{{\overset{arrow}{V}}_{{dcxy}{({O_{2} - {X_{2}Y_{2}}})}} = {V_{{dcxy}{({O - {XY}})}}^{j{({- \theta_{caxy}})}}}} \\{\approx \lbrack {{f \times 0 \times ( {r_{axy} - f} )^{- 1}} - {{fr}_{axy} \times 0 \times ( {r_{axy} - f} )^{- 2}}} \rbrack} \\{{^{j{({\theta_{axy} - \theta_{caxy}})}} + {( {1 + \beta} )f{\overset{.}{\theta}}_{axy}^{j{(\frac{\pi}{2})}}} - {( {1 + \beta} )f{\overset{.}{\theta}}_{caxy}^{j{(\frac{\pi}{2})}}}}} \\{\approx {{- ( {1 + \beta} )}{f( {{\overset{.}{\theta}}_{caxy} - {\overset{.}{\theta}}_{axy}} )}^{j{(\frac{\pi}{2})}}}}\end{matrix} & (14)\end{matrix}$

Therefore, the approximate theoretical formula of the image movementvelocity {right arrow over (V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎ in themoving coordinate system O₂-X₂Y₂ within the XY plane becomes theaforementioned expression (15). The component representing the directionof the image movement vector of the right side of expression (15) ise^(jπ/2), and therefore, the image movement direction is the Y₂-axisdirection in the direction at 90 degrees from the X₂-axis. {dot over(θ)}_(caxy) represents the rotation angular velocity around theprincipal point A, and {umlaut over (θ)}_(axy) represents the revolutionangular velocity of the principal point A around the origin O of thefixed coordinate system. β represents an imaging magnification of thisoptical system, and f represents the actual focal length. (1+β)frepresents an image side focal length. Therefore, this approximateexpression means that the image movement velocity in the Y₂ directionwithin the image pickup surface is −(image side focal length)×(valueobtained by subtracting the revolution angular velocity from therotation angular velocity).

With FIG. 14, the image movement theoretical formula of the presentinvention in the two-dimensional ZX coordinate system when the camera isprojected onto the ZX plane will be described. When the shake is a verysmall vibration movement with the initial state position as the center,the approximate conditions are such that ζ_(azx)≈0, ζ_(cazx)≈0,r_(azx)≈constant value, {dot over (r)}_(azx)≈0 and {umlaut over(r)}_(azx)≈0. From the approximate conditions, the approximatetheoretical formula of the image movement velocity {right arrow over(V)}_(dcxy(O) ₂ _(-X) ₂ _(Y) ₂ ₎ in the moving coordinate system O₂-Z₂X₂within the ZY plane is as the following expression (16) by the proceduresimilar to the approximate formula V_(dcxy(O2-X2Y2)) in the XY plane.

{right arrow over (V)}_(dczx(O) ₂ _(-Z) ₂ _(Y) ₂ ₎≈−(1+β)f({dot over(ζ)}_(cazx)−{dot over (ζ)}_(azx))e^(jπ/2)   (16)

The component representing the direction of the image blur vector of theright side of expression (16) is e^(jπ/2), and therefore, the imagemovement direction is the Z₂-axis direction in the direction at 90degrees from the X₂-axis. {dot over (ζ)}_(cazx) represents a rotationangular velocity around the principal point A, and {dot over (ζ)}_(azx)represents a revolution angular velocity of the principal point A aroundorigin O of the fixed coordinate system. β represents the imagingmagnification of this optical system, and f represents the actual focallength. (1+β)f represents the image side focal length. Therefore, theapproximate formula means that the image movement velocity in the X₂direction within the image pickup device surface is −(the image sidefocal length)×(value obtained by subtracting the revolution angularvelocity from the rotation angular velocity).

The output signal of the accelerometer 121 will be also described. Inthe XY coordinate plane, the revolution angular velocity at theprincipal point A can be expressed as follows.

{dot over (θ)}_(axy)=∫(acceleration component orthogonal to the linesegment r _(axy) at the point A)dt/r _(axy)

Therefore, the acceleration vector {umlaut over ({right arrow over(R)}_(a) can be measured and calculated. In this embodiment, theaccelerometer 121 is fixed to the point B, and therefore, theacceleration value at the point A needs to be obtained by calculationbased on the output of the accelerometer at the point B. Here, thedifference value between the acceleration at the point B and thatprincipal point A where the accelerometer is actually disposed, and thetheoretical acceleration value at the point B are obtained.Subsequently, the component (term) which is unnecessary in imagestabilization control is clarified.

First, an acceleration vector {umlaut over ({right arrow over(R)}_(a(O-XY)) which occurs at the principal point A in the fixedcoordinate system O-XY is obtained from the following expression (17).

$\begin{matrix}{{\overset{arrow}{\overset{¨}{R}}}_{a{({O - {XY}})}} = {{{\overset{¨}{r}}_{axy}{^{{j\theta}_{axy}}( {{first}\mspace{14mu} {term}\text{:}\mspace{14mu} {acceleration}\mspace{14mu} {component}\mspace{14mu} {of}\mspace{11mu} a\mspace{14mu} {change}\mspace{14mu} {in}\mspace{14mu} {length}\mspace{14mu} r_{a}} )}}\;  + {r_{axy}{\overset{.}{\theta}}_{axy}^{2}{^{j{({\theta_{axy} + \pi})}}( {{second}\mspace{14mu} {term}\text{:}\mspace{14mu} {centripetal}\mspace{14mu} {force}} )}} + {r_{axy}{\overset{¨}{\theta}}_{axy}{^{j{({\theta_{axy} + \frac{\pi}{2}})}}( {{third}\mspace{14mu} {term}\text{:}\mspace{14mu} {angular}\mspace{14mu} {acceleration}\mspace{14mu} {component}} )}} + {2{\overset{.}{r}}_{axy}{\overset{.}{\theta}}_{axy}{^{j{({\theta_{axy} + \frac{\pi}{2}})}}( {{fourth}\mspace{14mu} {term}\text{:}\mspace{14mu} {Coriolis}\mspace{14mu} {force}\mspace{14mu} {component}} )}} + {G\; {^{j{({\theta_{gxy} - \pi})}}( {{acceleration}\mspace{14mu} {component}\mspace{14mu} {of}\mspace{14mu} {the}\mspace{11mu} {gravity}\mspace{14mu} G} )}}}} & (17)\end{matrix}$

(Here, the gravity G works onto the accelerometer 121 as a reactionforce, and therefore, 180 degrees is subtracted from the angle θ_(gxy)representing the gravity direction.)

A relative acceleration {umlaut over ({right arrow over(R)}_(baxy(O-XY)) at the point B with respect to the principal point Ain the fixed coordinate system O-XY will be obtained. First, a relativeposition {right arrow over (R)}_(baxy(O-XY)) is obtained from thefollowing expression (18).

{right arrow over (R)} _(baxy(O-XY)) =r _(ba) e ^(j(θ) ^(ba) ^(+θ) ^(ca)⁾   (18)

If the first order derivative of expression (18) is performed by thetime t, the velocity vector can be obtained. Since the points A and Bare fixed to the same rigid body, a relative velocity {dot over ({rightarrow over (R)}_(baxy(O-XY)) is obtained from the following expression(19) from r_(baxy)=constant value, {dot over (r)}_(baxy)=0,θ_(baxy)=constant value, {dot over (θ)}_(baxy)=0, and {dot over(θ)}_(caxy)=rotation component (variable).

$\begin{matrix}\begin{matrix}{{\overset{\overset{arrow}{.}}{R}}_{{baxy}{({O - {XY}})}} = {{{\overset{.}{r}}_{baxy}^{j{({\theta_{baxy} + \theta_{caxy}})}}} + {{r_{baxy}( {{\overset{.}{\theta}}_{baxy} + {{\overset{.}{\theta}}_{caxy}\theta}} )}^{j{({\theta_{baxy} + \theta_{caxy} + \frac{\pi}{2}})}}}}} \\{= {{(0)^{{j\theta}_{baxy}}} + {{r_{baxy}( {0 + {\overset{.}{\theta}}_{caxy}} )}^{j{({\theta_{baxy} + \theta_{caxy} + \frac{\pi}{2}})}}}}} \\{= {r_{baxy}{\overset{.}{\theta}}_{caxy}^{j{({\theta_{baxy} + \theta_{caxy} + \frac{\pi}{2}})}}}}\end{matrix} & (19)\end{matrix}$

Next, the acceleration vector is obtained. The relative acceleration{umlaut over ({right arrow over (R)}_(baxy(O-XY)) at the point B(accelerometer position) with respect to the point A in the fixedcoordinate system O-XY is obtained from the following expression (20).

$\begin{matrix}{\begin{matrix}{{\overset{\overset{arrow}{¨}}{R}}_{{baxy}{({O - {XY}})}} = {{{\overset{¨}{r}}_{baxy}^{j{({\theta_{baxy} + \theta_{caxy}})}}} + {r_{baxy}( {{\overset{.}{\theta}}_{baxy} + {\overset{.}{\theta}}_{caxy}} )}^{2}}} \\{{^{j{({\theta_{baxy} + \theta_{caxy} + \pi})}} + {{r_{baxy}( {{\overset{¨}{\theta}}_{baxy} + {\overset{¨}{\theta}}_{caxy}} )}^{j{({\theta_{baxy} + \theta_{caxy} + \frac{\pi}{2}})}}} +}} \\{{2\; {{\overset{.}{r}}_{baxy}( {{\overset{.}{\theta}}_{baxy} + {\overset{.}{\theta}}_{caxy}} )}^{j{({\theta_{baxy} + \theta_{caxy} + \frac{\pi}{2}})}}}} \\{= {{0 \times ^{j{({\theta_{baxy} + \theta_{caxy}})}}} + {{r_{baxy}( {0 + {\overset{.}{\theta}}_{caxy}} )}^{2}^{j{({\theta_{baxy} + \theta_{caxy} + \pi})}}} +}} \\{{{{r_{baxy}( {0 + {\overset{¨}{\theta}}_{caxy}} )}^{j{({\theta_{baxy} + \theta_{caxy} + \frac{\pi}{2}})}}} +}} \\{{2 \times 0 \times ( {0 + {\overset{.}{\theta}}_{caxy}} )^{j{({\theta_{baxy} + \theta_{caxy} + \frac{\pi}{2}})}}}} \\{= {{{r_{baxy}( {\overset{.}{\theta}}_{caxy} )}^{2}^{j{({\theta_{baxy} + \theta_{caxy} + \pi})}}} + {r_{baxy}( {\overset{¨}{\theta}}_{caxy} )}^{2}}} \\{^{j{({\theta_{baxy} + \theta_{caxy} + \frac{\pi}{2}})}}}\end{matrix}\mspace{79mu} ( {= {{{centripetal}\mspace{14mu} {force}} + {{angular}\mspace{11mu} {acceleration}\mspace{14mu} {amount}}}} )} & (20)\end{matrix}$

The expression value is the movement vector error amount due to the factthat the accelerometer 121 is actually mounted at the position B withrespect to the principal point A which is an ideal position.

An acceleration vector {umlaut over ({right arrow over (R)}_(bxy(O-XY))at the point B in the fixed coordinate system O-XY is expressed by thesum of the vectors from the origin O to the principal point A alreadyobtained and from the principal point A to the point B. First, theposition vector {right arrow over (R)}_(bxy(O-XY)) at the point B in thefixed coordinate system O-XY is expressed by way of the principal pointA by the following expression (21).

Position Vector:

$\begin{matrix}\begin{matrix}{{\overset{arrow}{R}}_{{bxy}{({O - {XY}})}} = {r_{bxy}^{{j\theta}_{bxy}}}} \\{= {{\overset{arrow}{R}}_{axy} + {\overset{arrow}{R}}_{baxy}}} \\{= {{r_{axy}^{{j\theta}_{axy}}} + {r_{baxy}^{j{({\theta_{baxy} + \theta_{caxy}})}}}}}\end{matrix} & (21)\end{matrix}$

Velocity Vector:

$\begin{matrix}\begin{matrix}{{\overset{arrow}{\overset{.}{R}}}_{{bxy}{({O - {XY}})}} = {{{\overset{.}{r}}_{bxy}^{{j\theta}_{bxy}}} + {r_{bxy}{\overset{.}{\theta}}_{bxy}^{j{({\theta_{bxy} + \frac{\pi}{2}})}}}}} \\{= {{\overset{arrow}{\overset{.}{R}}}_{axy} + {\overset{arrow}{\overset{.}{R}}}_{baxy}}} \\{= {{{\overset{.}{r}}_{axy}^{{j\theta}_{axy}}} + {r_{axy}{\overset{.}{\theta}}_{axy}^{j{({\theta_{axy} + \frac{\pi}{2}})}}} + {r_{baxy}{\overset{.}{\theta}}_{caxy}^{j{({\theta_{baxy} + \theta_{caxy} + \frac{\pi}{2}})}}}}}\end{matrix} & (22)\end{matrix}$

Acceleration Vector:

$\begin{matrix}\begin{matrix}{{\overset{arrow}{\overset{¨}{R}}}_{{bxy}{({O - {XY}})}} = {{\overset{arrow}{\overset{¨}{R}}}_{axy} + {\overset{arrow}{\overset{¨}{R}}}_{baxy}}} \\{= {{{\overset{¨}{r}}_{axy}^{{j\theta}_{axy}}} + {r_{axy}{\overset{.}{\theta}}_{axy}^{2}^{j{({\theta_{axy} + \pi})}}} + {r_{axy}{\overset{¨}{\theta}}_{axy}^{j{({\theta_{axy} + \frac{\pi}{2}})}}} +}} \\{{{2{\overset{.}{r}}_{axy}{\overset{.}{\theta}}_{axy}^{j{({\theta_{axy} + \frac{\pi}{2}})}}} + {r_{baxy}{\overset{.}{\theta}}_{caxy}^{2}^{j{({\theta_{baxy} + \theta_{caxy} + \pi})}}} +}} \\{{{r_{baxy}{\overset{¨}{\theta}}_{caxy}^{j{({\theta_{baxy} + \theta_{caxy} + \frac{\pi}{2}})}}} + {Ge}^{j{({\theta_{gxy} - \pi})}}}}\end{matrix} & (23)\end{matrix}$

Next, an acceleration {umlaut over ({right arrow over (R)}_(bxy(O) ₂_(-X) ₂ _(Y) ₂ ₎ at the point B in the moving coordinate system O₂-X₂Y₂will be calculated. The latitude (scalar) of the acceleration desired tobe calculated is in the fixed coordinate system O-XYZ where the objectis present. Further, the acceleration is fixed to the moving coordinatesystem O₂-X₂Y₂, the three axes of the accelerometer 121 are oriented inthe X₂-axis direction, the Y₂-axis direction and the Z₂-axis direction,and the acceleration component needs to be expressed by the coordinateaxis directions of the moving coordinate system O₂-X₂Y₂Z₂.

The disposition state of the accelerometer 121 will be described indetail. The accelerometer 121 of three-axis outputs is disposed at thepoint B. In the moving coordinate system O₂-X₂Y₂Z₂, the axes of theaccelerometer are set to an accelerometer output A_(ccx2) with thesensitivity direction in the direction parallel with the X₂-axis, anaccelerometer output A_(ccy2) with the sensitivity direction in thedirection parallel with the Y₂ ⁻axis, and an accelerometer outputA_(ccz2) with the sensitivity direction in the direction parallel withthe Z₂-axis. Since the movement in the XY plane is described here, theaccelerometer output A_(ccx2) and the accelerometer output A_(ccy2) willbe described.

In order to obtain the acceleration {umlaut over ({right arrow over(R)}_(bxy(O-X) ₂ _(Y) ₂ ₎ by converting the acceleration {umlaut over({right arrow over (R)}_(bxy(O-XY)) at the point B in the fixedcoordinate system O-XY obtained in the above into the components in theX₂-axis and Y₂-axis direction with the origin O as it is, the coordinateconversion may be performed in the direction opposite to the rotationangle θ_(caxy) of the camera. Therefore, the following expression (24)is established.

Accelerometer Output:

$\begin{matrix}{{\overset{arrow}{A}}_{{cc}{({O - {X_{2}Y_{2}}})}} = {{{\overset{arrow}{\overset{¨}{R}}}_{{bxy}{({O - {XY}})}}^{j{({- \theta_{caxy}})}}} = {{{\overset{¨}{r}}_{axy}{^{j{({\theta_{axy} - \theta_{caxy}})}}( {{first}\mspace{14mu} {term}\text{:}\mspace{14mu} {optical}\mspace{14mu} {axis}\mspace{14mu} {direction}\mspace{20mu} {movement}} )}} + {r_{axy}{\overset{.}{\theta}}_{axy}^{2}{^{j{({\theta_{axy} - \theta_{caxy} + \pi})}}( {{second}\mspace{14mu} {term}\text{:}\mspace{14mu} {centripetal}\mspace{14mu} {force}\mspace{14mu} {of}\mspace{14mu} {revolution}} )}} + {r_{axy}{\overset{¨}{\theta}}_{axy}{^{j{({\theta_{axy} - \theta_{caxy} + \frac{\pi}{2}})}}( {{third}\mspace{14mu} {term}\text{:}\mspace{14mu} {acceleration}\mspace{14mu} {of}\mspace{14mu} {revolution}} )}} + {2{\overset{.}{r}}_{axy}{\overset{.}{\theta}}_{axy}{^{j{({\theta_{axy} - \theta_{caxy} + \frac{\pi}{2}})}}( {{fourth}\mspace{14mu} {term}\text{:}\mspace{14mu} {Coriolis}\mspace{14mu} {force}} )}} + {r_{baxy}{\overset{.}{\theta}}_{caxy}^{2}{^{j{({\theta_{baxy} + \theta_{caxy} - \theta_{caxy} + \pi})}}( {{fifth}\mspace{14mu} {term}\text{:}\mspace{14mu} {centripetal}\mspace{14mu} {force}\mspace{14mu} {of}\mspace{14mu} {revolution}} )}} + {r_{baxy}{\overset{¨}{\theta}}_{caxy}{^{j{({\theta_{baxy} + \theta_{caxy} - \theta_{caxy} + \frac{\pi}{2}})}}( {{sixth}\mspace{14mu} {term}\text{:}\mspace{14mu} {acceleration}\mspace{14mu} {of}\mspace{14mu} {rotation}} )}} + {{Ge}^{j{({\theta_{gxy} - \pi - \theta_{caxy}})}}( {{seventh}\mspace{14mu} {term}\text{:}\mspace{14mu} {gravity}\mspace{14mu} {acceleration}\mspace{14mu} {component}} )}}}} & (24)\end{matrix}$

The approximate formula is obtained by substituting the approximateconditions. Restriction conditions are given such that the revolutionangular velocity {dot over (θ)}_(axy) and the rotation angular velocity{dot over (θ)}_(caxy) are very small vibration (±) around 0 so thatθ_(axy)≈0 and θ_(caxy)≈0. Further, it is assumed that the scalar r_(axy)changes very slightly so that {dot over (r)}_(axy)=finite value, {umlautover (r)}_(axy)=finite value, θ_(baxy) substantially satisfiesπ/2−π/4≦θ_(baxy)≦π/2+π/4.

Accelerometer Output:

$\begin{matrix}{{{\overset{arrow}{A}}_{{cc}{({O - {X_{2}Y_{2}}})}} = {{{\overset{arrow}{\overset{¨}{R}}}_{{bxy}{({O - {XY}})}}^{j{({- \theta_{caxy}})}}} \approx {{{\overset{¨}{r}}_{axy}{^{j{({0 - 0})}}( {{first}\mspace{14mu} {term}\text{:}\mspace{14mu} {optical}\mspace{14mu} {axis}\mspace{14mu} {direction}\mspace{20mu} {movement}} )}} + {r_{axy}{\overset{.}{\theta}}_{axy}^{2}{^{j{({0 - 0 + \pi})}}( {{second}\mspace{14mu} {term}\text{:}\mspace{14mu} {centripetal}\mspace{14mu} {force}\mspace{14mu} {of}\mspace{14mu} {revolution}} )}} + {r_{axy}{\overset{¨}{\theta}}_{axy}{^{j{({0 - 0 + \frac{\pi}{2}})}}( {{third}\mspace{14mu} {term}\text{:}\mspace{14mu} {acceleration}\mspace{14mu} {of}\mspace{14mu} {revolution}} )}} + {2{\overset{.}{r}}_{axy}{\overset{.}{\theta}}_{axy}{^{j{({0 - 0 + \frac{\pi}{2}})}}( {{fourth}\mspace{14mu} {term}\text{:}\mspace{14mu} {Coriolis}\mspace{14mu} {force}} )}}}}}{{r_{baxy}{\overset{.}{\theta}}_{caxy}^{2}{^{j{({\theta_{baxy} + 0 + \pi})}}( {{fifth}\mspace{14mu} {term}\text{:}\mspace{14mu} {centripetal}\mspace{14mu} {force}\mspace{14mu} {of}\mspace{14mu} {revolution}} )}} + {r_{baxy}{\overset{¨}{\theta}}_{caxy}{^{j{({\theta_{baxy} + 0 + \frac{\pi}{2}})}}( {{sixth}\mspace{14mu} {term}\text{:}\mspace{14mu} {acceleration}\mspace{14mu} {of}\mspace{14mu} {rotation}} )}} + {{Ge}^{j{({\theta_{gxy} - \pi - 0})}}( {{seventh}\mspace{14mu} {term}\text{:}\mspace{14mu} {gravity}\mspace{14mu} {acceleration}\mspace{14mu} {component}} )}}} & (25)\end{matrix}$

This real part is the accelerometer output A_(ccx2) in the X₂-axisdirection, and the imaginary part is the accelerometer output A_(ccy2)in the Y₂-axis direction. The above described polar coordinate systemrepresentation is decomposed into the X₂ component and the Y₂ componentin the orthogonal coordinate system representation.

Accelerometer Output in the X₂-Axis Direction:

$\begin{matrix}{{\overset{arrow}{A}}_{{ccx}_{2}{({o - {X_{2}Y_{2}}})}} \approx {{{+ {\overset{¨}{r}}_{axy}}\mspace{14mu} ( {{first}\mspace{14mu} {term}\text{:}\mspace{14mu} {optical}\mspace{14mu} {axis}\mspace{14mu} {direction}\mspace{14mu} {movement}} )} - {r_{axy}{\overset{.}{\theta}}_{axy}^{2}\mspace{14mu} ( {{second}\mspace{14mu} {term}\text{:}\mspace{14mu} {centripetal}\mspace{14mu} {force}\mspace{14mu} {of}\mspace{14mu} {revolution}} )} + {r_{baxy}{\overset{.}{\theta}}_{caxy}^{2}{\cos ( {\theta_{baxy} + \pi} )}} + ( {{fifth}\mspace{14mu} {term}\text{:}\mspace{14mu} {centripetal}\mspace{14mu} {force}\mspace{14mu} {of}\mspace{14mu} {rotation}} ) + {r_{baxy}{\overset{¨}{\theta}}_{caxy}^{2}{\cos ( {\theta_{baxy} + {\pi/2}} )}\mspace{14mu} ( {{sixth}\mspace{14mu} {term}\text{:}\mspace{14mu} {acceleration}\mspace{14mu} {of}\mspace{14mu} {rotation}} )} + {G\; {\cos ( {\theta_{gxy} - \pi} )}\mspace{14mu} ( {{seventh}\mspace{14mu} {term}\text{:}\mspace{14mu} {gravity}\mspace{14mu} {acceleration}\mspace{14mu} {component}} )}}} & (26)\end{matrix}$

In expression (26), only the first term {umlaut over (r)}_(axy) isneeded for optical axis direction movement correction. The second term,the fifth term, the sixth term and the seventh term are componentsunnecessary for the optical axis direction movement correction, andunless they are erased, they become the error components when theacceleration {umlaut over (r)}_(axy) in the direction of the X₂-axiswhich is the optical axis is obtained. The second, the fifth, the sixthand the seventh terms can be erased by the similar method as the case ofthe next expression (27).

In order to delete the second term (centripetal force of revolution),the values of r_(axy) and {dot over (θ)}_(axy) are included in thesecond term need to be obtained. r_(axy) is substantially equal to theobject side focal length (1+β)f/β (where β represents an imagingmagnification). The image pickup apparatus in recent years is equippedwith the focus encoder which measures the moving position of theautofocus lens 140. Therefore, it is easy to calculate the objectdistance from the output value of the focus encoder, in the focus state.As a result, r_(axy) is obtained. The value obtained from the nextexpression (27) is used as the revolution angular velocity {dot over(θ)}_(axy).

Accelerometer Output in the Y₂-Axis Direction:

$\begin{matrix}{{{\overset{arrow}{A}}_{{ccy}_{2}}( {O - {X_{2}Y_{2}}} )} \approx {{{+ {jr}_{axy}}{{\overset{¨}{\theta}}_{axy}( {{third}\mspace{14mu} {term}\text{:}\mspace{14mu} {acceleration}\mspace{14mu} {of}\mspace{14mu} {revolution}} )}} + {j\; 2\; {\overset{.}{r}}_{axy}{{\overset{.}{\theta}}_{axy}( {{fourth}\mspace{14mu} {term}\text{:}\mspace{14mu} {Coriolis}\mspace{14mu} {force}} )}} + {{jr}_{baxy}{\overset{.}{\theta}}_{caxy}^{2}{\sin ( {\theta_{baxy} + \pi} )}( {{fifth}\mspace{14mu} {term}\text{:}\mspace{14mu} {centripetal}\mspace{14mu} {force}\mspace{14mu} {of}\mspace{14mu} {rotation}} )} + {{jr}_{baxy}{\overset{¨}{\theta}}_{caxy}{\sin ( {\theta_{baxy} + \frac{\pi}{2}} )}( {{sixth}\mspace{14mu} {term}\text{:}\mspace{14mu} {acceleration}\mspace{14mu} {of}\mspace{14mu} {rotation}} )} + {{jG}\; {\sin ( {\theta_{gxy} - \pi} )}( {{seventh}\mspace{14mu} {term}\text{:}\mspace{11mu} {gravity}\mspace{14mu} {acceleration}\mspace{14mu} {component}} )}}} & (27)\end{matrix}$

The respective terms of the accelerometer output A_(ccy2(O-X2Y2)) in theY₂-axis direction will be described. The third term jr_(axy){umlaut over(θ)}_(axy) is the component necessary for obtaining the revolutionangular velocity {dot over (θ)}_(axy) desired to be obtained in thepresent embodiment, and the revolution angular velocity {dot over(θ)}_(axy) is obtained by dividing the third term with the known r_(axy)and integrating the result. The fourth term j2{dot over (r)}_(axy){dotover (θ)}_(axy) represents a Coriolis force. If the movement of thecamera in the optical axis direction is small, {dot over (r)}_(axy)≈0 isestablished, and the fourth term can be ignored. The fifth term and thesixth term are the error components which are included in theaccelerometer output A_(ccy2(O-X2Y2)) since the accelerometer 121 cannotbe disposed at the ideal principal point position A and is disposed atthe point B.

The fifth term jr_(baxy){dot over (θ)}_(caxy) ² sin(θ_(baxy)+π)represents the centripetal force which occurs since the accelerometer121 rotates around the principal point A. r_(baxy) and θ_(baxy) are thecoordinates of the point B at which the accelerometer 121 is mounted,and are known. {dot over (θ)}_(caxy) represents the rotation angularvelocity, and is the value which can be measured with the angularvelocity sensor 130 mounted on the camera. Therefore, the value of thefifth term can be calculated.

The sixth term jr_(baxy){umlaut over (θ)}_(caxy) sin(θ_(baxy)π/2)represents the acceleration component when the accelerometer 121 rotatesaround the principal point A, and r_(baxy) and θ_(baxy) are thecoordinates of the point B at which the accelerometer 121 is mounted,and are known. {umlaut over (θ)}_(caxy) can be calculated bydifferentiating the value of the angular velocity sensor 130 mounted onthe camera. Therefore, the value of the sixth term can be calculated.

The seventh term jG sin(θ_(gxy)−π) is the influence of the gravityacceleration, and can be dealt as a constant in the approximate formula,and therefore, can be erased by filtering processing of a circuit.

As described above, the accelerometer output A_(ccy2(O-X2Y2)) in theY₂-axis direction includes unnecessary components for revolution angularvelocity {dot over (θ)}_(axy) which is desired to be obtained in thepresent invention. However, it has become clear that the unnecessarycomponent can be subtracted by calculation according to the output ofthe angular velocity sensor 130 disposed at the camera and the mountingposition information of the accelerometer 121 with respect to theprincipal point A, and the necessary revolution angular velocity {dotover (θ)}_(axy) can be obtained.

Similarly, from the accelerometer output A_(ccx2(O-X2Y2)) in the X₂direction, the movement velocity {dot over (r)}_(axy) in thesubstantially optical axis direction of the camera is desired to becalculated. The first term {umlaut over (r)}_(axy) corresponds to theoptical axis direction movement acceleration. The second term, the fifthterm, the sixth term and the seventh term can be erased for the samereason as described with the accelerometer output A_(ccy2(O-X2Y2)) inthe Y₂-axis direction. Therefore, the movement velocity {dot over(r)}_(axy) substantially in the optical axis direction of the camera canbe obtained from the accelerometer output A_(ccx2(O-X2Y2)) in the X₂direction.

The above described content will be concretely described with referenceto FIG. 15. FIG. 15 illustrates a diagram of a lens barrel illustratinga change of the principal position of the shooting optical system 105corresponding to the change of the imaging magnification. With a changeof the imaging magnification β of the shooting optical system 105incorporated in the lens barrel 102, the principal point A of theshooting optical system 105 moves from A1 when the image magnificationis equal-magnification (as the time of proximity shooting) to A2 at thetime of infinity shooting (β=0.0). Here, the accelerometer 121 isdisposed at a position in the lens barrel 102 which corresponds to theprincipal point position A1 when the image magnification is theequal-magnification in terms of the optical axis direction. In thisstate, shooting is performed with the imaging magnification β=0.5. Thedistance in the optical direction between the principal position A3 ofthe shooting optical system 105 at the time of shooting and theaccelerometer 121 becomes larger by ΔX as compared with the principalpoint position A1 at the time of equal-magnification, and therefore, thedistance between the principal point of the shooting optical system 105and the accelerometer 121 changes to r_(A1A3) (=r_(baxy) in expression(27)) from ΔY (ΔY<r_(A1A3)). The error components, which are the fifthterm and the sixth term in expression (27), change correspondingly tothe change. If this change amount is left as it is, the revolutionangular velocity {dot over (θ)}_(axy) is calculated with the errorcomponents of the fifth term and the sixth term left in the revolutionangular velocity {dot over (θ)}_(axy) which is desired to be obtained inthe present invention, and therefore, accurate blur correction cannot bemade. Therefore, as described in the present invention, the unnecessaryterms need to be removed from the output of the accelerometer 121 basedon the output of the accelerometer 121 and the position of the principalpoint A (or the imaging magnification β) of the shooting optical system105.

When the user is to perform shooting with the imaging magnificationβ=0.9 in FIG. 15, for example, if the principal point position hardlymoves from A1, θ_(baxy)≈π/2 is satisfied, and therefore,sin(θ_(baxy)+π/2) in the sixth term of expression (27) is such thatsin(θ_(baxy)+π/2)≈sin(π). Therefore, the sixth term can be regarded aszero. More specifically, the sixth term does not have to be consideredas an error component. In such a case, according to the result of theimaging magnification β calculated in flowchart S1050 illustrated inFIGS. 3A and 3B, only the fifth term is calculated and is subtractedfrom the accelerometer output A_(ccy2(O-X2Y2)) in the Y₂-axis directionat the time of removal of the error component of expression (27) whichis performed in S1090, whereby the necessary revolution angular velocity{dot over (θ)}_(axy) can be obtained. Thereby, the calculating time forblur correction can be shortened, and therefore, more accurate blurcorrection can be performed.

Apart from this, when the angular blur is small, {dot over (θ)}_(caxy) ²in the fifth term jr_(baxy){dot over (θ)}_(caxy) ² sin(θ_(baxy)+π)becomes substantially zero, and therefore, the fifth term can beregarded as zero. More specifically, the fifth term does not have to beconsidered as an error component. Therefore, according to the outputresult of the angular velocity sensor 130, it can be determined whetherthe fifth term needs to be subtracted as an error component. In such acase, according to the output value of the angular velocity sensor 130which is read in S1060 of the flowchart illustrated in FIGS. 3A and 3B,only the sixth term is calculated, and subtracted from the accelerometeroutput A_(ccy2(O-X2Y2)) in the Y₂-axis direction at the time of removalof the error component of expression (27) which is performed in S1090,whereby the necessary revolution angular velocity {dot over (θ)}_(axy)be obtained. Thereby, the calculating time of blur correction can beshortened, and therefore, more accurate blur correction can beperformed.

Here, in order to verify the effect of the present invention, theexperiment as follows was performed. First, at the time of shooting anobject, the actual movement amount is measured with a laser displacementmeter. The movement correction amount is calculated by using the outputsof the accelerometer 121 and the angular velocity sensor 131 at thattime, and the difference (called a residual movement) from the actualmovement amount is obtained.

At this time, to what extent the difference occurs to the residualmovement amount depending on the presence or absence of removal of theaforementioned unnecessary terms from the output of the accelerometer121 was confirmed. The result of the simulation is illustrated in FIG.16. In FIG. 16, the broken line represents the actual movement amount,the solid line represents the residual movement amount in the case ofperforming movement correction by removing the unnecessary terms fromthe output of the accelerometer 121 (hereinafter, called “correcting theoutput”), and the two-dot chain line represents the residual movementamount in the case of performing movement correction without removingthe unnecessary terms from the output of the accelerometer 121(hereinafter, called “without correcting the output”). The axis ofordinates represents displacement, and the axis of abscissa represents ashutter speed in shooting.

As is obvious from FIG. 16, when the output of the accelerometer 121 isnot corrected, only about 25% of the actual movement amount can becorrected, for example, when the shutter speed is 1/20 sec, whereas whenthe output of the accelerometer 121 is corrected, about 55% of theactual movement amount can be corrected when the shutter speed is 1/20sec. More specifically, it can be confirmed that by correcting theoutput of the accelerometer 121 according to the change of the principalpoint position of the shooting optical system 105, the movementcorrection effect is enhanced.

In embodiment 1, when the ratio of the revolution angular velocity tothe rotation angular velocity is 0.1 or less, the revolution angularvelocity is sufficiently small with respect to the rotation angularvelocity, and therefore, the image stabilization calculation issimplified by performing only rotation movement correction, which leadsto enhancement in speed, and reduction in power consumption.

Further, when exposure of shooting is started by fully depressing therelease button not illustrated, the revolution angular velocity in realtime is estimated by multiplying the ratio of the revolution angularvelocity to the past rotation angular velocity by the rotation angularvelocity in real time. Thereby, even if the output of the accelerometer121 is disturbed by shutter shock and operation vibration of the cameraat the time of shooting, use of a revolution acceleration value which issignificantly erroneous can be prevented, and stable image blurcorrection is enabled.

Further, an angular movement and a parallel movement are newly andstrictly modeled and expressed mathematically to be a rotation movementand a revolution movement, and thereby, whatever state the two movementcomponent states may be, accurate image stabilization without a controlfailure can be performed. Further, the relative positional informationbetween the principal point position of the shooting optical system andthe accelerometer is calculated, and the error component with respect tothe blur correction is removed. Therefore, accurate image stabilizationcorresponding to the change of the principal point position of theshooting optical system can be performed. Further, the error componentof the blur correction is removed from the stored value of the relativepositional information of the principal point position of the shootingoptical system and the accelerometer, and therefore, accurate imagestabilization corresponding to the change of the principal pointposition of the shooting optical system can be performed while thecalculation processing amount is reduced. Further, image stabilizationis performed based on the difference between the rotation angularvelocity and the revolution angular velocity, and therefore, thecalculation processing amount after difference calculation can bereduced. Further, the units of the rotation movement and the revolutionmovement are the same (for example: rad/sec), and therefore, calculationbecomes easy. Further, the image movement in the image pickup surface ofthe image pickup device, and the optical axis direction movement can berepresented by the same expression, and therefore, image movementcorrection calculation and the optical axis direction movementcorrection calculation can be performed at the same time.

Embodiment 2

By using FIGS. 17A and 17B, embodiment 2 will be described. The sameflow as in FIGS. 3A and 3B according to embodiment 1 is included.Therefore, the same reference numerals and characters are used for thesame flow, and the description will be omitted.

After revolution angular velocity calculation of S1100 in FIGS. 17A and17B, the flow proceeds to S2610. In S2610, it is determined whether theimaging magnification of shooting is 0.2 or more (predetermined value ormore). In the case of the imaging magnification being 0.2 or more, theflow proceeds to S2620, and in the case of the imaging magnificationbeing less than 0.2 (less than the predetermined value), the flowproceeds to S1130. In S1130, rotation movement correction calculation isperformed as in embodiment 1.

In S2620, it is determined whether or not the revolution angularvelocity with respect to the rotation angular velocity is between −0.9and +0.9 (within ranges between predetermined values). If it is within±0.9, the flow proceeds to S1120. When it is less than −0.9 or exceeds+0.9, the flow proceeds to S2630.

In S2630, the angular velocity ratio is fixed (stored) to the constant(specified constant) of 0.9, and in the next S2640, estimation of thepresent revolution angular velocity is calculated by multiplying therotation angular velocity obtained in real time by the fixed angularvelocity ratio of 0.9, and the flow proceeds to the next S1120. InS1120, the rotation revolution difference movement correctioncalculation is performed as in embodiment 1.

In embodiment 2, when the imaging magnification is less than 0.2, therevolution angular velocity is sufficiently small with respect to therotation angular velocity, and therefore, the image stabilizationcalculation is simplified by only performing rotation movementcorrection, which leads to enhancement in speed and reduction in powerconsumption. Further, the ratio of the revolution angular velocity tothe rotation angular velocity rarely exceeds one, and when the ratioexceeds ±0.9, the ratio is fixed to the constant 0.9, whereby erroneousexcessive correction is prevented.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2009-139171, filed on Jun. 10, 2009, which is hereby incorporated byreference herein in its entirety.

1. An image stabilization apparatus, comprising: a shooting opticalsystem that shoots an object, in which a principal point of the shootingoptical system moves in an optical axis direction of the shootingoptical system; an angular velocity detector that detects an angularvelocity applied to the image stabilization apparatus and outputs theangular velocity; an acceleration detector that detects an accelerationapplied to the image stabilization apparatus and outputs theacceleration; a calculation unit that calculates a position of aprincipal point of the shooting optical system; a first angular velocitycalculation unit that calculates a first angular velocity componentabout the position of the principal point based on an output of theangular velocity detector; a second angular velocity calculation unitthat calculates a second angular velocity component based on an outputof the acceleration detector, a calculation result of the firstacceleration calculation unit and the position of the principal point;and a controlling unit that performs image stabilization control basedon a difference between the first angular velocity component and thesecond angular velocity component.
 2. The image stabilization apparatusaccording to claim 1, further comprising an angular velocity ratiocalculation unit that calculates an angular velocity ratio of the secondangular velocity component which is corrected to the first angularvelocity component, wherein the controlling unit performs imagestabilization control based on a difference between the first angularvelocity component and the second angular velocity component when theangular velocity ratio is larger than a predetermined value, andperforms image stabilization control based on the first angular velocitycomponent when the angular velocity ratio is the predetermined value orless.
 3. An image pickup apparatus, comprising the image stabilizationapparatus according to claim
 1. 4. An image stabilization apparatus,comprising: a shooting optical system that shoots an object; an angularvelocity detector that detects an angular velocity applied to the imagestabilization apparatus and outputs the angular velocity; anacceleration detector that detects an acceleration applied to the imagestabilization apparatus and outputs the acceleration; a principal pointcalculation unit that calculates a position of a principal point of theshooting optical system; a rotation angular velocity calculation unitthat calculates a rotation angular velocity component about theprincipal point of the shooting optical system based on an output of theangular velocity detector; a revolution angular velocity calculationunit that calculates a revolution angular velocity component about theobject based on the output of the acceleration detector and acalculation result of the rotation angular velocity calculation unit,and corrects the calculated revolution angular velocity componentaccording to the position of the principal point calculated by theprincipal point calculation unit; and a controlling unit that performsimage stabilization control based on a difference between the rotationangular velocity component and the revolution angular velocity componentwhich is corrected.
 5. The image stabilization apparatus according toclaim 4, further comprising: a memory unit that stores a correctionvalue by which the revolution angular velocity component is correctedaccording to the position of the principal point calculated by theprincipal point calculation unit.
 6. The image stabilization apparatusaccording to claim 4, further comprising: a memory unit that stores acorrection formula for correcting the revolution angular velocitycomponent according to the position of the principal point calculated bythe principal point calculation unit.
 7. The image stabilizationapparatus according to claim 5, wherein the memory unit stores relativepositional information of the position of the principal point of theshooting optical system and the acceleration detector.
 8. The imagestabilization apparatus according to claim 7, wherein the calculatedrevolution angular velocity component is corrected by at least any oneof a first correction component calculated by a relative positioncalculated from the relative positional information and the rotationangular velocity component, and a second correction component calculatedfrom the relative position calculated from the relative positionalinformation and a derivative value of the rotation angular velocitycomponent.
 9. The image stabilization apparatus according to claim 4,further comprising a rotation revolution difference calculation unitthat calculates a rotation revolution difference value based on thedifference between the rotation angular velocity component and thecorrected revolution angular velocity component, wherein the controllingunit performs image stabilization control based on the rotationrevolution difference value.
 10. The image stabilization apparatusaccording to claim 4, further comprising a rotation revolution angularvelocity ratio calculation unit that calculates a rotation revolutionangular velocity ratio of the corrected revolution angular velocitycomponent to the rotation angular velocity component, wherein therevolution angular velocity calculation unit calculates estimation ofthe revolution angular velocity component by a product of a rotationangular velocity component calculated in real time and the rotationrevolution angular velocity ratio calculated by the rotation revolutionangular velocity ratio calculation unit.
 11. The image stabilizationapparatus according to claim 10, wherein the rotation revolution angularvelocity ratio calculation unit sets the rotation revolution angularvelocity ratio to be a specified constant when the rotation revolutionangular velocity ratio exceeds a predetermined value.
 12. The imagestabilization apparatus according to claim 10, wherein the controllingunit performs image stabilization control based on the rotationrevolution difference value when the rotation revolution angularvelocity ratio is larger than a predetermined value, and performs imagestabilization control based on the rotation angular velocity componentwhen the rotation revolution angular velocity ratio is the predeterminedvalue or less.
 13. The image stabilization apparatus according to claim10, wherein the controlling unit performs image stabilization controlbased on the rotation revolution difference value when an imagingmagnification of the shooting optical system is a predetermined value ormore, and performs image stabilization control based on the rotationangular velocity component when the imaging magnification of theshooting optical system is less than the predetermined value.
 14. Theimage stabilization apparatus according to claim 4, further comprising:an optical axis direction acceleration detector that detects an opticalaxis direction component of an acceleration applied to the imagestabilization apparatus; and an optical axis direction image stabilizingcontrol unit that corrects an optical axis direction component of amovement applied to the image stabilization apparatus, wherein theoptical axis direction image stabilizing control unit performs anoptical axis direction image stabilization control based on the opticalaxis direction component of the acceleration.
 15. An image pickupapparatus, comprising the image stabilization apparatus according toclaim 4.